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Regression Analysis 
 Explain the impact of one variable on another 
Independent variable: 
the variable used to explain ...
Regression Analysis 
Independent variable 
Dependent variable 
is also used to 
x-axis 
y-axis 
Simple Linear 
Quantify l...
Regression Analysis 
Independent variable 
Dependent variable 
is also used to 
x-axis 
y-axis 
Simple Linear 
Quantify l...
Linear Regression Example 
Scatterplot 
 House price model: scatter plot 
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House price model: scatter plot and regression line 
y = 0.1098x + 98.248 
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House price model: scatter plot and regression line 
y = 0.1098x + 98.248 
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y = 0.1098x + 98.248 R² = 0.5808 
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Standard Error of Estimate 
 The standard deviation of the 
observations around the 
regression line. 
When predicting, t...
y = 0.1098x + 98.248 R² = 0.5808 
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An Overview of Simple Linear Regression

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An Overview of Simple Linear Regression

  1. 1. Regression Analysis  Explain the impact of one variable on another Independent variable: the variable used to explain the dependent variable Dependent variable the variable you wish to explain is used to x-axis y-axis Simple Linear independent Annual Salary vs. Education $0 $20,000 $40,000 $60,000 $80,000 $100,000 $120,000 0 2 4 6 8 10 Annual salary Years of Education (past high school) ?
  2. 2. Regression Analysis Independent variable Dependent variable is also used to x-axis y-axis Simple Linear Quantify linear relationships …develop an equation for the… Y = mX + b value of Y when X = 0 change in Y relative to a change in X Y = b1X + b0 slope intercept The purpose of regression analysis is calculate estimates of the slope and intercept.
  3. 3. Regression Analysis Independent variable Dependent variable is also used to x-axis y-axis Simple Linear Quantify linear relationships …develop an equation for the… Y = mX + b value of Y when X = 0 change in Y relative to a change in X Y = b1X + b0 slope intercept The purpose of regression analysis is calculate estimates of the slope and intercept. =INTERCEPT(y-range, x-range) =SLOPE(y-range, x-range) using LEAST SQUARES ESTIMATION
  4. 4. Linear Regression Example Scatterplot  House price model: scatter plot 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 Square Feet House Price ($1000s) (1) Describe the relationship… r = 0.762
  5. 5. House price model: scatter plot and regression line y = 0.1098x + 98.248 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 Price in $1000s sqft Selling Price vs. Square Feet trendline (2) Model the Data… Calculate the regression coefficients and interpret b0 is the estimated mean value of Y when the value of X is 0 (if X = 0 is in the range of observed X values) Because the square footage of the house cannot be 0, the Y intercept has no practical application. slope intercept
  6. 6. House price model: scatter plot and regression line y = 0.1098x + 98.248 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 Price in $1000s sqft Selling Price vs. Square Feet trendline (2) Model the Data… Calculate the regression coefficients and interpret b1 measures the mean change in the average value of Y as a result of a one-unit change in X The mean value of a house increases by 0.1098($1000) = $109.80, on average, for each additional one square foot of size slope intercept
  7. 7. y = 0.1098x + 98.248 R² = 0.5808 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 Price in $1000s sqft Selling Price vs. Square Feet (3) Evaluate the Model… Calculate R2 58% of the variability in the PRICE of a home is exaplined by using the SIZE of the home.
  8. 8. Standard Error of Estimate  The standard deviation of the observations around the regression line. When predicting, this is the stdev of the predictions (3) Evaluate the Model… Calculate R2 and std error
  9. 9. y = 0.1098x + 98.248 R² = 0.5808 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 Price in $1000s sqft Selling Price vs. Square Feet (3) Evaluate the Model… Calculate R2 and std error SYX=41.33

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