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The future is uncertain. Some events do have a very small probability of happening, like an asteroid destroying the earth. So we accept that tomorrow will come as a certain event. But future demand for a business’s goods and services is very uncertain. Yet, the management of a company wants to have some idea of the survival (or growth) of the company in the future. Should they expect to hire more people or let some go? Should they plan to increase capacity? How much investment is needed for future assets, or should they down size? Forecasting provides some ideas about the future, but how this is accomplished can vary from company to company. And one key factor is how accurate the forecast is. Generally, the further into the future one looks, the more uncertain the information is. How do forecasters reduce their forecasting errors? How much error is tolerable? Another key factor in forecasting is data availability. Data processing and storage capability have become extremely available and inexpensive. Software and computing power is also very cheap. Collecting real-time sales data via point-of-sales systems is now common at most retail establishments. But couple this with a situation in companies that have a large number of products, such as a retail store or a large manufacturing company with hundreds or thousands of product numbers and/or product lines, forecasting becomes complicated. Forecasting Methods There are two main types or genres of forecasting methods, qualitative and quantitative. The former consists of judgment and analysis of qualitative factors, such as scenario building and scenario analysis. The latter is obviously based on numerical analysis. This genre of forecasting includes such methods as linear regression, time series analysis, and data mining algorithms like CHAID and CART, which are useful especially in the growing world of artificial intelligence and machine learning in business. This module will look at the linear regression and time series analysis using exponential smoothing. Linear Growth When using any mathematical model, we have to consider which inputs are reasonable to use. Whenever we extrapolate, or make predictions into the future, we are assuming the model will continue to be valid. There are different types of mathematical model, one of which is linear growth model or algebraic growth model and another is exponential growth model, or geometric growth model. The constant change is the defining characteristic of linear growth. Plotting the values, we can see the values form a straight line, the shape of linear growth. If a quantity starts at size P0 and grows by d every time period, then the quantity after n time periods can be determined using either of these relations: Recursive form: Pn = Pn-1 + d Explicit form: Pn = P0 + d n In this equation, d represents the common difference – the amount that the population changes each time n increases by 1. Calculating values using the explicit form and plot ...
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Week 4 Lecture 12 Significance Earlier we discussed correlations without going into how we can identify statistically significant values. Our approach to this uses the t-test. Unfortunately, Excel does not automatically produce this form of the t-test, but setting it up within an Excel cell is fairly easy. And, with some slight algebra, we can determine the minimum value that is statistically significant for any table of correlations all of which have the same number of pairs (for example, a Correlation table for our data set would use 50 pairs of values, since we have 50 members in our sample). The t-test formula for a correlation (r) is t = r * sqrt(n-2)/sqrt(1-r2); the associated degrees of freedom are n-2 (number of pairs – 2) (Lind, Marchel, & Wathen, 2008). For some this might look a bit off-putting, but remember that we can translate this into Excel cells and functions and have Excel do the arithmetic for us. Excel Example If we go back to our correlation table for salary, midpoint, Age, Perf Rat, Service, and Raise, we have: Using Excel to create the formula and cell numbers for our key values allows us to quickly create a result. The T.dist.2t gives us a p-value easily. The formula to use in finding the minimum correlation value that is statistically significant is r = sqrt(t^2/(t^2 + n-2)). We would find the appropriate t value by using the t.inv.2T(alpha, df) with alpha = 0.05 and df = n-2 or 48. Plugging these values into the gives us a t-value of 2.0106 or 2.011(rounded). Putting 2.011 and 48 (n-2) into our formula gives us a r value of 0.278; therefore, in a correlation table based on 50 pairs, any correlation greater or equal to 0.278 would be statistically significant. Technical Point. If you are interested in how we obtained the formula for determining the minimum r value, the approach is shown below. If you are not interested in the math, you can safely skip this paragraph. t = r* sqrt(n-2)/sqrt(1-r2) Multiplying gives us t *sqrt (1- r2) = r2* (n-2) Squaring gives us: t2 * (1- r2) = r2* (n-2) Multiplying out gives us: t2– t2* r2 = n r2-2* r2 Adding gives us: t2= n* r2-2*r2+ t2 *r2 Factoring gives us t2= r2 *(n -2+ t2) Dividing gives us t2 / (n -2+ t2) = r2 Taking the square root gives us r = sqrt (t2 / (n -2+ t2) Effect Size Measures As we have discussed, there is a difference between statistical and practical significance. Virtually any statistic can become statistically significant if the sample is large enough. In practical terms, a correlation of .30 and below is generally considered too weak to be of any practical significance. Additionally, the effect size measure for Pearson’s correlation is simply the absolute value of the correlation; the outcome has the same general interpretation as Cohen’s D for the t-test (0.8 is strong, and 0.2 is quite weak, for example) (Tanner & Youssef- Morgan, 2013). Spearman’s Rank Correlation Another typ.
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BUS 308 – Week 4 Lecture 2 Interpreting Relationships Expected Outcomes After reading this lecture, the student should be able to: 1. Interpret the strength of a correlation 2. Interpret a Correlation Table 3. Interpret a Linear Regression Equation 4. Interpret a Multiple Regression Equation Overview As in many detective stories, we will often find that when one thing changes, we see that something else has changed as well. Moving to correlation and regression opens up new insights into our data sets, but still lets us use what we have learned about Excel tools in setting up and generating our results. The correlation between events is mirrored in data analysis examinations with correlation analysis. This week’s focus changes from detecting and evaluating differences to looking at relationships. As students often comment, finding significant differences in gender-based measures does not explain why these differences exist. Correlation, while not always explaining why things happen gives data detectives great clues on what to examine more closely and helps move us towards understanding why outcomes exist and what impacts them. If we see correlations in the real world, we often will spend time examining what might underlie them; finding out if they are spurious or causal. Regression lets us use relationships between and among our variables to predict or explain outcomes based upon inputs, factors we think might be related. In our quest to understand what impacts the compa-ratio and salary outcomes we see, we have often been frustrated due to being basically limited to examining only two variables at a time, when we felt that we needed to include many other factors. Regression, particularly multiple regression, is the tool that allows us to do this. Linear Correlation When two things seem to move in a somewhat predictable way, we say they are correlated. This correlation could be direct or positive, both move in the same direction, or it could be inverse or negative, where when one increases the other decreases. The Law of Supply in economics is a common example of an inverse (or negative) correlation, where the more supply we have of something, the less we typically can charge for it; the Law of Demand is an example of a direct (or positive) correlation as the more demand exists for something, the more we can charge for it. Height and weight in young children is another common example of a direct correlation, as one increases so does the other measure. Probably the most commonly used correlation is the Pearson Correlation Coefficient, symbolized by r. It measures the strength of the association – the extent to which measures change together – between interval or ratio level measures as well as the direction of the relationship (inverse or direct). Several measures in our company data set could use the Pearson Correlation to show relationships; salary and midpoint, salary and yea.
BUS 308 – Week 4 Lecture 2 Interpreting Relationships .docx
BUS 308 – Week 4 Lecture 2 Interpreting Relationships .docx
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BUS 308 – Week 4 Lecture 2 Interpreting Relationships Expected Outcomes After reading this lecture, the student should be able to: 1. Interpret the strength of a correlation 2. Interpret a Correlation Table 3. Interpret a Linear Regression Equation 4. Interpret a Multiple Regression Equation Overview As in many detective stories, we will often find that when one thing changes, we see that something else has changed as well. Moving to correlation and regression opens up new insights into our data sets, but still lets us use what we have learned about Excel tools in setting up and generating our results. The correlation between events is mirrored in data analysis examinations with correlation analysis. This week’s focus changes from detecting and evaluating differences to looking at relationships. As students often comment, finding significant differences in gender-based measures does not explain why these differences exist. Correlation, while not always explaining why things happen gives data detectives great clues on what to examine more closely and helps move us towards understanding why outcomes exist and what impacts them. If we see correlations in the real world, we often will spend time examining what might underlie them; finding out if they are spurious or causal. Regression lets us use relationships between and among our variables to predict or explain outcomes based upon inputs, factors we think might be related. In our quest to understand what impacts the compa-ratio and salary outcomes we see, we have often been frustrated due to being basically limited to examining only two variables at a time, when we felt that we needed to include many other factors. Regression, particularly multiple regression, is the tool that allows us to do this. Linear Correlation When two things seem to move in a somewhat predictable way, we say they are correlated. This correlation could be direct or positive, both move in the same direction, or it could be inverse or negative, where when one increases the other decreases. The Law of Supply in economics is a common example of an inverse (or negative) correlation, where the more supply we have of something, the less we typically can charge for it; the Law of Demand is an example of a direct (or positive) correlation as the more demand exists for something, the more we can charge for it. Height and weight in young children is another common example of a direct correlation, as one increases so does the other measure. Probably the most commonly used correlation is the Pearson Correlation Coefficient, symbolized by r. It measures the strength of the association – the extent to which measures change together – between interval or ratio level measures as well as the direction of the relationship (inverse or direct). Several measures in our company data set could use the Pearson Correlation to show relationships; salary and midpoint, salary and yea ...
BUS 308 – Week 4 Lecture 2 Interpreting Relationships .docx
BUS 308 – Week 4 Lecture 2 Interpreting Relationships .docx
jasoninnes20
Week 3 Lecture 11 Regression Analysis Regression analysis is the development of an equation that shows the impact of the independent variables (the inputs we can generally control) on the output result. While the mathematical language may sound strange, most of you are quite familiar with regression like instructions and use them quite regularly. To make a cake, we take 1 box mix, add 1¼ cups of water, ½ cup of oil, and 3 eggs. All of this is combined and cooked. The recipe is an example of a regression equation. The output (or result or dependent variable) is the cake, the inputs (or independent variables) are the inputs used. Each input is accompanied by a coefficient (AKA weight or amount) that tells us how “much” of the variable is “used” or weighted into the outcome. So, in an equation format, this cake recipe might look like: Y = 1X1 + 1.25X2 + .5X3 + 3X4 where: Y = cake X1 = box mix X2 = cups of water X3 = cups of oil X4 = an egg. Of course, for the cake, the recipe needs to go through the cooking process; while for other regression equations the outputs need to go through whatever “process” turns the inputs into the output – this is often called “life.” Example With a regression analysis, we can identify what factors influence an outcome. So, with our Salary issue, the natural question to help us answer our research question of do males and females get equal pay for equal work would be: what factors influence or explain an individual’s pay? This is a perfect question for a multi-variate regression. Multi-variate simply means we have multiple input variables with a single output variable (Lind, Marchel, & Wathen, 2008). Variables. A regression analysis uses two distinct types of data. The first are variables that are at least interval level or better (the same as the other techniques we have used so far). The other is called a dummy variable, a variable that can be coded 0 or 1 indicating the presence of some characteristic. In our data set, we have two variables that can be used as dummy coded variables in a regression, Degree and Gender; both coded 0 or 1. In the case of Degree, the 0 stands for having a bachelor’s degree and the 1 stands for having an advanced degree. For Gender, 0 means a male and 1 means a female. How these are interpreted in a regression output will be discussed below. For now, the significance of dummy coding is that it allows us to include nominal or ordinal data in our analysis. Excel Approach. For our question of what factors influence pay, we will use Excel’s Regression function found in the Data Analysis section. This function will produce two output tables of interest. The first table tests to see if the entire regression equation is statistically significant; that is, do the input variables significantly impact the output variable. If so, we would then examine the second table – the coefficients used in a regression equation for e.
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BUS 308 Week 4 Lecture 3 Developing Relationships in Excel Expected Outcomes After reading this lecture, the student should be able to: 1. Calculate the t-value for a correlation coefficient 2. Calculate the minimum statistically significant correlation coefficient value. 3. Set-up and interpret a Linear Regression in Excel 4. Set-up and interpret a Multiple Regression in Excel Overview Setting up correlations and regressions in Excel is fairly straightforward and follows the approaches we have seen with our previous tools. This involves setting up the data input table, selecting the tools, and inputting information into the appropriate parts of the input window. Correlations Question 1 Data set-up for a correlation is perhaps the simplest of any we have seen. It involves simply copying and pasting the variables from the Data tab to the Week 4 worksheet. Again, paste them to the right of the question area. The screenshot below has the data for both the question 1 correlation and the question 2 multiple regression pasted them starting at column V. You can paste all the data at once or add the multiple regression variables later (as long as you do not sort the original data). Specifically, for Question 1, copy the salary data to column V (for example). Then copy the Midpoint thru Service columns and paste them next to salary. Finally copy the Raise column and paste it next to the service column. Notice that our data input range for this question now includes Salary in Column V and the other interval level variables found in Columns W thru AA. Question 1 asks for the correlation among the interval/ratio level variables with salary and says to exclude compa-ratio. For our example, we will correlation compa-ratio with the other interval/ratio level variables with the exclusion of salary. Since compa-ratio equals the salary divided by the midpoint, it does not seem reasonable to use salary in predicting compa- ratio or compa-ratio in predicting salary. Pearson correlations can be performed in two ways within Excel. If we have a single pair of variables we are interested in, for example compa-ratio and performance rating, we could use the fx (or Formulas) function CORREL(array1, array2) (note array means the same as range) to give us the correlation. However, if we have several variables we want to correlate at the same time, it is more effective to use the Correlation function found in the Analysis ToolPak in the Data Analysis tab. Set up of the input data for Correlation is simple. Just ensure that all of the variables to be correlated are listed together, and only include interval or ratio level data. For our data set, this would mean we cannot include gender or degree; even though they look like numerical data the 0 and 1 are merely labels as far as correlation is concerned. In the Correlation data input box shown below, list the entire data range, indicate if your dat ...
BUS 308 Week 4 Lecture 3 Developing Relationships in Exc.docx
BUS 308 Week 4 Lecture 3 Developing Relationships in Exc.docx
ShiraPrater50
Numerical approximation
Numerical approximation
Lizeth Paola Barrero
Measures and Strengths of Association Remember that while we may find two variables to be involved in a relationship, we also want to know the strength of the association. Each type of variable has its own measure to determine this though. Three measures will be discussed in this paper, Lambda, Gamma, and Pearson’s r. Lambda Lambda is a measure of association which should be used when both variables are nominal. Essentially this means that knowing a person’s attribute on one variable will help you guess their attribute on the other (Babbie et al., 2014). Gamma Gamma is used to explore the relationship between two ordinal variables. It can also be used to measure association between one dichotomous nominal and one ordinal variable (Babbie et al., 2014, p. 227). Unlike lambda, gamma indicates a strength of an association and a direction. The closer to -1.00 or +1.00, the stronger the relationship, whereas the closer to 0 the weaker the relationship. You can determine the direction of a relationship the following way: A negative association is indicated by a negative sign. This means that as one variable increases the other decreases- the variables are moving away from each other. For example, as social class increases, prejudice decreases. On the other hand, a positive association, indicated by a plus or positive sign, means that both variables change in the same direction, either increase or decrease. For example, as social class increases, so too does prejudice or as social class decreases, so too does prejudice. Correlation Coefficient- Pearson’s r Pearson’s r, also known as the correlation coefficient, is the test measure used to determine the association between interval/ratio variables. This measure is similar to Gamma in how it can be understood and establish direction of association. Value of Measures of Association 0.00 + or - .01 to .09 + or - .10 to .29 + or - .30 to .99 Strength of Association None- no assocation at all Weak- uninteresting association Moderate- worth making note of Evidence of a strong association- extremely interesting Perfect- strongest association possible 1.00 Measures of Association in SPSS Analyze – Descriptive Statistics – Crosstabs Place your dependent variable in the Row and your independent variable in the Column. Click "Statistics" to choose which test you will run for the measure/strength of association. You will select Lambda for nominal variables, Gamma for ordinal variables (or one ordinal and one dichotomous nominal), or Pearson’s r for interval/ratio variables. Measures of Association in SPSS- Understanding Output Lambda The test above is looking at the relationship between one’s political affiliation and their race. We look at the value .036, which is the measure when political party is the DV (see in table). This means that we can improve our guessing of political affiliation by 4% if we know that person’s race. Based on our notes abo ...
Measures and Strengths of AssociationRemember that while w.docx
Measures and Strengths of AssociationRemember that while w.docx
ARIV4
Applied Econometrics and Economic Modeling
Lecture2 Applied Econometrics and Economic Modeling
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stone55
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Applied Econometrics and Economic Modeling
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For this assignment, use the aschooltest.sav dataset. The dataset consists of Reading, Writing, Math, Science, and Social Studies test scores for 200 students. Demographic data include gender, race, SES, school type, and program type. Instructions: Work with the aschooltest.sav datafile and respond to the following questions in a few sentences. Please submit your SPSS output either in your assignment or separately. 1. Identify an Independent and Dependent Variable (of your choice) and develop a hypothesis about what you expect to find. ( note: the IV is a grouping variable, which means it needs to have more than 2 categories and the DV is continuous) 2. Run Assumption tests for Normality and initial Homogeneity of Variance. What are your results? 3. Run the one-way ANOVA with the Levene test & Tukey post hoc test. a. What are the results of the Levene test? What does this mean? b. What are the results of the one-way ANOVA (use notation)? What does it mean? c. Are post hoc tests necessary? If so, what are the results of those analyses? 4. How do your analyses address your hypotheses? Is concentration of single parent families associated with reading scores? Using the AECF state data, the regression below measures the effect of the state's percentage of single parent families on the percentage of 4th graders with below basic reading scores. %belowbasicread = β0 + β1x%SPF + u Stata Output 1) Please write out the regression equation using the coefficients in the table 2) Please provide an interpretation of the coefficient for SPF 3) How does the model fit? 4) What is the NULL hypothesis for a T test about a regression coefficient? 5) What is the ALTERNATE hypothesis for a T test about a regression coefficient? 6) Look at the p value for the coefficient SPF. a) Report the p value b) How many stars would it get if we used our standard convention? * p ≤ .1 ** p ≤ .05 *** p ≤ .01 image1.png Two-Variable (Bivariate) Regression In the last unit, we covered scatterplots and correlation. Social scientists use these as descriptive tools for getting an idea about how our variables of interest are related. But these tools only get us so far. Regression analysis is the next step. Regression is by far the most used tool in social science research. Simple regression analysis can tell us several things: 1. Regression can estimate the relationship between x and y in their original units of measurement. To see why this is so useful, consider the example of infant mortality and median family income. Let’s say that a policymaker is interested in knowing how much of a change in median family income is needed to significantly reduce the infant mortality rate. Correlation cannot answer this question, but regression can. 2. Regression can tell us how well the independent variable (x) explains the dependent variable (y). The measure is called the R square. Simple Tw ...
For this assignment, use the aschooltest.sav dataset.The d
For this assignment, use the aschooltest.sav dataset.The d
MerrileeDelvalle969
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
What is Multiple Linear Regression and How Can it be Helpful for Business Ana...
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Smarten Augmented Analytics
- Constructed a mathematical model using Multiple Regression to estimate the Selling price of the house based on a set of predictor variables. - SAS was used for Variable profiling, data transformations, data preparation, regression modeling, fitting data, model diagnostics, and outlier detection.
Prediction of house price using multiple regression
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vinovk
I am sharing the notes of regression model to have an complete idea about it.
Detail Study of the concept of Regression model.pptx
Detail Study of the concept of Regression model.pptx
truptikulkarni2066
Two-Variable (Bivariate) Regression In the last unit, we covered scatterplots and correlation. Social scientists use these as descriptive tools for getting an idea about how our variables of interest are related. But these tools only get us so far. Regression analysis is the next step. Regression is by far the most used tool in social science research. Simple regression analysis can tell us several things: 1. Regression can estimate the relationship between x and y in their original units of measurement. To see why this is so useful, consider the example of infant mortality and median family income. Let’s say that a policymaker is interested in knowing how much of a change in median family income is needed to significantly reduce the infant mortality rate. Correlation cannot answer this question, but regression can. 2. Regression can tell us how well the independent variable (x) explains the dependent variable (y). The measure is called the R square. Simple Two-Variable (Bivariate) Regression Regression uses the equation of a line to estimate the relationship between x and y. You may remember back in algebra learning about the equation of a line. Some learned it as Y =s X + K or Y = mX + B. In statistics, we use a different form: Equation 1: Y = B0 + B1X + u Let’s define each term in the equation: · Y is the dependent variable. It is placed on the Y (vertical) axis. In the example below, the dependent variable (Y) is the infant mortality rate. · B0 is the Y intercept. B0 is also referred to as “the constant.” B0 is the point where the regression line crosses the Y axis. Importantly, B0 is equal to the predicted value of Ywhen X=0. In most cases, B0 is does not get much attention for two reasons. First, the researcher is usually interested in the relationship between x and y. not the relationship between x and y at the single value of x=0. Second, often independent variables do not take on the value zero. Consider the AECF sample data. There are no states with low-birth-weight percentages equal to zero, so we would be extrapolating beyond what the data tell us. · B1 is usually the main point of interest for researchers. It is the slope of the line relating x to y. Researchers usually refer to B1 as a slope coefficient, regression coefficient or simply a coefficient. B1 measures the change in Y for a one-unit change in x. We represent change by the symbol ∆. B1 = · u is the error term. The error term is the distance between the regression line and the dots on the scatterplot. Think about it, regression estimates a single line through the cloud of data. Naturally, the line does not hit all the data points. The degree to which the line “misses” the data point is the error. u can also be thought of as all the other factors that affect the infant mortality rate besides X. Importantly, we assume that u is totally random given X. The ...
Two-Variable (Bivariate) RegressionIn the last unit, we covered
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For this assignment, use the aschooltest.sav dataset.The d
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Lecture8 Applied Econometrics and Economic Modeling
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