final revision

1. General revision
(Q1) State whether the following statements are true or false and give a brief explanation
1. If the value of the linear correlation coefficient is zero, then these two variables
are independent.
2. The least square regression line minimizes the sum of errors.
3. The covariance between any two variables decides the strength of their relation.
4. The regression coefficient decides the trend and the strength of the relation
between the dependent and the independent variables.
(Q2) Define the following terms briefly.
1. The determinant coefficient.
2. The deterministic model and the probabilistic model.
(Q3) Answer the following questions briefly.
Explain the meaning of independent and dependent variables for a regression model. Explain
the difference between a simple and a multiple regression model.
1. Compare between the roles of both the regression coefficient and the correlation
coefficient. Can the values of regression coefficient and the correlation coefficient
have different signs? Explain.
2. The similarities and the difference between the normal, the standard normal.
3. Can the values of the regression coefficient and the correlation
coefficient have different signs? Explain.
4. If the correlation coefficient between two variables equals zero,
then the two variables are independent. Comment.
5. Why is the random error included in a regression model?
Question (1):
The following table gives the experience (in years) and the number of
computers sold during the previous three months by seven salespersons.
Experience
( years)
4 12 9 6 10 16 7
Computer sold
{unit)
19 42 28 31 39 35 21
(a) Find the suitable least squares regression line.
(b) Give a brief interpretation of the values of the Y-intercept and slope calculated
in the previous part.
(c) Calculate the correlation coefficient and the determinant coefficient. Explain
what they mean.
(d) Predict the number of computers sold during the past three months by
salespersons with eleven years experience.

2. Question (2):
A jeans manufacturer knows that a large budget for television advertising (x)
of his product will create a demand (y) for it among department store buyers. In
a sample of eight years we obtain the following data.
  920
x  124500
x2
  885
y  115075
y2
The regression coefficient of y on x (b) = 0.94
Using the previous information calculate
(1) The correlation coefficient (r) and comment on the result.
(2) The determinant coefficient (
2
R ) and comment on the result.
(3) Predict the demand (y) when the budget for television advertising (x)
equals 10.
Question (3):
Scores on the sales aptitude test are approximately normally distributed, with a mean
of 500 and a variance of 625. The head of a personal has decided to extend job to
those in the top 15% and to discard the files of those in the bottom 60%.
1) What is the cutoff for a job offer?
2) What is the cutoff for discarding?
Question (4):
A charity believes that when it puts out an appeal for charitable donations the donations it
receives will normally distributed with a mean $ 50 and standard deviation $ 6, and it is assumed
that donations will be independent of each other.
1) Find the probability that the first donation it receives will be greater than $ 60.
2) Find the value X such that 5% of donations are more than $ X.
Problem 5:
The management of a supermarket wants to adopt a new promotional policy of giving
free gift to every customer who spends more than a certain amount per visit at this
supermarket. The expectation of the management is that after this promotional policy is
advertised, the expenditure for all customers at this supermarket will be normally
distributed with mean $95 and a standard deviation of $21.
a) If the management wants to give free gifts to at most 8% of the customers, what
should the amount be above which a customer would receive a free gift?
b) In a sample of 100 customers, what are the number of customers whose expenditure
is between $74 and $137?
c) In a sample of 25 customers, what is the probability of choosing a customer whose
expenditure is between $90 and $101?
Question (6):
The following data represents the grades of a sample of 12 students in statistics and
economics as follows
Math grade A C B B D B F F D C B C
Economic Grade B F C B C A C F B B A C
Calculate the correlation between the student's grade in math and economics. What its type
and strength.

3. Question (7):
In a study of the relation between the expanding budget of advertisement on a
specific product (X) in thousand of pounds and the quantity sold (Y), in tons, of a
product. A sample of the advertising budget and the quantity sold in eight successive
months is drawn from on of the companies which are dealing in such a product and the
following information is obtained.

   

   





8
1
i
i
i
8
1
i
8
1
i
8
1
i
2
i
8
1
i
i
2
i
i
1850
Y
X
1650
Y
,
110
Y
,
2150
X
,
130
X
Using the previous information calculate
1) The correlation coefficient (r) and the determinant coefficient ( 2
R ). Comment on
the result.
2) Find the regression line of Y on X and interpret the meaning of its intercept and
regression coefficient.
3) Predict the number of tones sold from this product if the expended advertising
budget in one month is 25 thousand pounds.
Question (8):
The balances of all saving accounts at a local bank have a normal distribution with its
mean equal to $ 12450 and standard deviation equal to $ 4160. Find the probability that
balance of a sample of 50 saving accounts selected from this bank will be
(a) More than $ 11500.
(b) Within $ 1500 of the population mean.
(c) Find the number of accounts which will have an account of more than the
population mean by at least $ 1000.
Question (9):
Fast Auto service provides oil and lube for cars. It is known that the mean time taken for
oil and lube service at this garage is 15 minutes per car with a standard deviation of 2.4
minutes. The management wants to promote the business guaranteeing a maximum waiting
time for customers. If a customer's car is not served with that period, the customers will
receive a 50% discount on the charge. The company wants to limit this discount to at most
5% of the customers. What should the maximum guaranteed waiting time be? Assume that
the times taken for oil and lube service for all cars have a normal distribution.
Question (10):
In a study of the relation between the experience (in years) (x) and the number of
computers sold (y) during the last three months, we draw a sample of seven sales persons and
obtain the following results
    


 6820
y
2084
y
x
210
y
63
x 2
i
i
i
i
i
The correlation coefficient ( r ) = 0.89
Find:
a) Find the suitable least squares regression line.
b) Give a brief interpretation of the values of the Y-intercept and slope calculated in
the previous part.

4. c) Calculate the determinant coefficient and interpret its value.
d) Predict the number of computers sold during the past three months by salespersons
with twenty years experience.