a.
What has been the sample size for the above?
b.
Perform a t-test and determine whether or not x and y are related. Use = 0.05.
c.
Perform an F-test and determine whether or not x and y are related. Use = 0.05.
d.
Compute the coefficient of determination.
e.
Interpret the meaning of the value of the coefficient of determination that you found in d. Be
very specific.
a.
22
b.
Since the test statistic t = 2.1 > 2.086, reject Ho. Therefore, x and y are related.
c.
Since the test statistic F = 4.41 > 4.35, reject Ho.
d.
0.1807
e.
18.07% of the variation in y is due to the variation in x.
11. Given below are seven observations collected in a regression study on two variables, x (independent
variable) and y (dependent variable). Use Excel’s Regression Tool to answer the following questions.
x
y
2
12
3
9
6
8
7
7
8
6
7
5
9
2
a.
What is the estimated regression equation?
b.
Perform a t test and determine whether or not x and y are related. Use = 0.05.
c.
Perform an F test and determine whether or not x and y are related. Use = 0.05.
d.
Find and interpret the coefficient of determination.
x
y
2
3
9
6
8
7
7
8
6
7
5
9
2
SUMMARY OUTPUT
Multiple R
0.9185587
R Square
0.84375
Observations
7
Regression
Residual
Total
Intercept
b.
Since the p-value 0.003478165 .05, reject Ho. Therefore, x and y are related.
c.
Since the p-value 0.00348 .05, reject Ho.
12. A company has recorded data on the weekly sales for its product (y) and the unit price of the
competitor’s product (x). The data resulting from a random sample of 7 weeks follows. Use Excel’s
Regression Tool to answer the following questions.
Week
Price
Sales
1
.33
20
2
.25
14
3
.44
22
4
.40
21
5
.35
16
6
.39
19
7
.29
15
a.
What is the estimated regression equation?
b.
Perform a t test and determine whether or not x and y are related. Use = 0.05.
c.
Perform an F test and determine whether or not x and y are related. Use = 0.05.
d.
Find and interpret the coefficient of determination.
20
14
22
21
16
19
15
SUMMARY OUTPUT
13. Given below are seven observations collected in a regression study on two variables, x (independent
variable) and y (dependent variable). Use Excel to
a.
compute a 95% confidence interval for E(y) when x = 5
b.
compute a 95% prediction interval for y when x = 5.
x
y
2
12
3
9
6
8
7
7
8
6
7
5
9
2
Value Sheet
Given value of x
xbar
x-xbar
Sum of (x-xbar)sq
Multiple R
R Square
Adjusted R Sq.
Standard Error
Observations
Regression
Residual
Total
Intercept
b.
Since the p-value 0.009385 < .05, reject Ho. Therefore, the competitor’s price and sales are related.
Since the p-value 0.009385 < .05, reject Ho.
price
14. A company has recorded data on the weekly sales for its product (y) and the unit price of the
competitor’s product (x). The data resulting from a random sample of 7 weeks follows. Use Excel to:
a.
compute a 95% confidence interval for expected sales for all weeks when the competitor’s
price is .30.
b.
compute a 95% prediction interval for sales for a week when the competitor’s price is .30.
Week
Price
Sales
1
.33
20
2
.25
14
3
.44
22
4
.40
21
5
.35
16
6
.39
19
7
.29
15
Value Sheet
Given value of x
xbar
x-xbar
Sum of (x-xbar)sq
Var of yhat
Stdev of yhat
t value
Margin of Error
SUMMARY OUTPUT
Multiple R
R Square
Var of yind
Adjusted R Square
Stdev of yind
Standard Error
Observations
Formula Sheet
Given value of x
0.3
Xbar
=AVERAGE(A2:A8)
x-xbar
=E2-E3
=E4^2
Sum of (x-xbar)sq
=DEVSQ(A2:A8)
Stdev of yhat
=SQRT(E7)
t value
=T.INV(0.05,5)
Margin of Error
=E9*E8
=B28+B29*E2
=E11-E10
=E11+E10
Var of yind
=D24+E7
Stdev of yind
=SQRT(E16)
=E9*E17
=E11-E18
=E11+E19
14.00 to 18.13
b.
11.36 to 27.42
15. Given below are seven observations collected in a regression study on two variables, x (independent
variable) and y (dependent variable). Use Excel’s Regression Tool to construct a residual plot and use
it to determine if any model assumption have been violated.
x
y
2
12
3
9
6
8
7
7
8
6
7
5
9
2
16. A company has recorded data on the weekly sales for its product (y) and the unit price of the
competitor’s product (x). The data resulting from a random sample of 7 weeks follows. Use Excel’s
Regression Tool to construct a residual plot and use it to determine if any model assumption have been
violated.
Week
Price
Sales
1
.33
20
2
.25
14
3
.44
22
4
.40
21
5
.35
16
6
.39
19
7
.29
15
17. Given below are seven observations collected in a regression study on two variables, x (independent
variable) and y (dependent variable). Use Excel’s Regression Tool to construct a residual plot and use
it to determine if any model assumption have been violated.
x
y
2
12
3
9
6
8
7
7
8
6
7
5
9
2
18. Connie Harris, in charge of office supplies at First Capital Mortgage Corp., would like to predict the
quantity of paper used in the office photocopying machines per month. She believes that the number
of loans originated in a month influence the volume of photocopying performed. She has compiled
the following recent monthly data:
Number of Loans
Originated in Month
Sheets of Photocopy
Paper Used (000’s)
45
22
25
13
50
24
60
25
40
21
25
16
35
18
40
25
a. Develop the least-squares estimated regression equation that relates sheets of photocopy paper used
to loans originated.
b. Use the regression equation developed in part (a) to forecast the amount of paper used in a month
when 42 loan originations are expected.
c. Compute SSE, SST, and SSR.
d. Compute the coefficient of determination r2. Comment on the goodness of fit.
e. Compute the correlation coefficient.
f. Compute the mean square error MSE.
g. Compute the standard error of the estimate.
h. Compute the estimated standard deviation of b1.
i. Use the t test to test the following hypothesis b1 = 0 at a = .05.
j. Develop a 95% confidence interval estimate for b1 to test the hypothesis b1 = 0.
k. Use the F test to test the hypothesis b1 = 0 at a .05 level of significance.
l. Develop a 95% confidence interval estimate of the mean number of sheets of paper used when 38
mortgages are originated.
m. Develop a 95% prediction interval estimate for the number of sheets of paper used when 38
mortgages are originated.
19. Scott Bell Builders would like to predict the total number of labor hours spent framing a house based
on the square footage of the house. The following data has been compiled on ten houses recently
built.
Square
Footage
(100s)
Framing
Labor
Hours
Square
Footage
(100s)
Framing
Labor
Hours
20
195
27
225
21
170
29
240
23
220
31
225
23
200
32
275
26
230
35
260
a. Develop the least-squares estimated regression equation that relates framing labor hours to house
square footage.
b. Use the regression equation developed in part (a) to predict framing labor hours when the house size
is 3350 square feet.
20. Assume you have noted the following prices for books and the number of pages that each book
contains.
Book
Pages (x)
Price (y)
A
500
$7.00
B
700
7.50
C
750
9.00
D
590
6.50
E
540
7.50
F
650
7.00
G
480
4.50
a.
Develop a least-squares estimated regression line.
b.
Compute the coefficient of determination and explain its meaning.
c.
Compute the correlation coefficient between the price and the number of pages. Test to see
if x and y are related. Use = 0.10.
t = 2.54 > 2.015 (df = 5); p–value is between .05 and 0.1; (Excel’s results: p-value of 0.052);
21. Assume you have noted the following prices for books and the number of pages that each book
contains.
Book
Pages (x)
Price (y)
A
500
$7.00
B
700
7.50
C
750
9.00
D
590
6.50
E
540
7.50
F
650
7.00
G
480
4.50
a.
Perform an F test and determine if the price and the number of pages of the books are related.
Let = 0.01.
b.
Perform a t test and determine if the price and the number of pages of the books are related.
Let = 0.01.
c.
Develop a 90% confidence interval for estimating the average price of books that contain 800
pages.
d.
Develop a 90% confidence interval to estimate the price of a specific book that has 800 pages.
$7.29 to $10.63 (rounded)
d.
$5.62 to $12.31 (rounded)
22. The following data represent the number of flash drives sold per day at a local computer shop and their
prices.
Price (x)
Units Sold (y)
$34
3
36
4
32
6
35
5
30
9
38
2
40
1
a.
Develop a least-squares regression line and explain what the slope of the line indicates.
b.
Compute the coefficient of determination and comment on the strength of relationship
between x and y.
c.
Compute the sample correlation coefficient between the price and the number of flash drives
sold. Use = 0.01 to test the relationship between x and y.
b.
conclude x and y are related
23. The following data represent the number of flash drives sold per day at a local computer shop and their
prices.
Price (x)
Units Sold (y)
$34
3
36
4
32
6
35
5
30
9
38
2
40
1
a.
Perform an F test and determine if the price and the number of flash drives sold are related.
Let = 0.01.
b.
Perform a t test and determine if the price and the number of flash drives sold are related.
Let = 0.01.
related
t = -5.4428 < -4.032; p-value .01; (Excel’s result: p-value = .0028); reject Ho, x and y are
24. Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable)
and X (independent variable).
ANOVA
df
SS
Regression
1
110
Residual
8
74
Total
9
184
Coefficients
Standard Error
Intercept
39.222
5.943
x
-0.5556
0.1611
a.
What has been the sample size for the above?
b.
Perform a t test and determine whether or not X and Y are related. Let = 0.05.
c.
Perform an F test and determine whether or not X and Y are related. Let = 0.05.
d.
Compute the coefficient of determination.
e.
Interpret the meaning of the value of the coefficient of determination that you found in d. Be
very specific.
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
x
59.783% of the variability in Y is explained by the variability in X.
25. Shown below is a portion of a computer output for regression analysis relating Y (dependent variable)
and X (independent variable).
ANOVA
df
SS
Regression
1
24.011
Residual
8
67.989
Coefficients
Standard Error
Intercept
11.065
2.043
x
-0.511
0.304
a.
What has been the sample size for the above?
b.
Perform a t test and determine whether or not X and Y are related. Let = 0.05.
c.
Perform an F test and determine whether or not X and Y are related. Let = 0.05.
d.
Compute the coefficient of determination.
e.
Interpret the meaning of the value of the coefficient of determination that you found in d. Be
very specific.
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
x
26.1% of the variability in Y is explained by the variability in X.
26. Part of an Excel output relating X (independent variable) and Y (dependent variable) is shown below.
Fill in all the blanks marked with “?”.
Summary Output
Regression Statistics
Multiple R
0.1347
R Square
?
Adjusted R Square
?
Standard Error
3.3838
Observations
?
ANOVA
df
SS
MS
F
Significance F
Regression
?
2.7500
?
?
0.632
Residual
?
?
11.45
Total
14
?
Coefficients
Standard Error
t Stat
P-value
Intercept
8.6
2.2197
?
0.0019
x
0.25
0.5101
?
0.632
Summary Output
Multiple R
R Square
Adjusted R Square
Standard Error
3.384
Observations
ANOVA
Regression
1
2.750
0.2402
0.6322
Residual
13
148.850
11.45
Total
14
151.600
Coefficients
Standard Error
t Stat
Intercept
8.6
2.2197
3.8744
0.0019
x
0.25
0.5101
0.4901
0.6322
27. Shown below is a portion of a computer output for a regression analysis relating Y (dependent
variable) and X (independent variable).
ANOVA
df
SS
Regression
1
115.064
Residual
13
82.936
Total
Coefficients
Standard Error
Intercept
15.532
1.457
x
-1.106
0.261
a.
Perform a t test using the p-value approach and determine whether or not Y and X are related.
Let = 0.05.
b.
Using the p-value approach, perform an F test and determine whether or not X and Y are
related.
c.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.
Multiple R
0.7623
R Square
0.5811
Adjusted R Square
0.5489
Standard Error
2.5258
Observations
Regression
Residual
Total
Intercept
x
c.
58.11% of the variability in Y is explained by the variability in X.
28. Part of an Excel output relating X (independent variable) and Y (dependent variable) is shown below.
Fill in all the blanks marked with “?”.
Summary Output
Regression Statistics
Multiple R
?
R Square
0.5149
Adjusted R Square
?
Standard Error
7.3413
Observations
11
ANOVA
df
SS
MS
F
Significance F
Regression
?
?
?
?
0.0129
Residual
?
?
?
Total
?
1000.0000
Coefficients
Standard Error
t Stat
P-value
Intercept
?
29.4818
3.7946
0.0043
x
?
0.7000
-3.0911
0.0129
R Square
Adjusted R Square
Standard Error
Observations
Regression
1
514.9455
9.5546
0.0129
Residual
Total
10
1000.0000
Intercept
29.4818
3.7946
0.0043
x
0.7000
-3.0911
0.0129
29. Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X
(unit price).
ANOVA
df
SS
Regression
1
5048.818
Residual
46
3132.661
Total
47
8181.479
Coefficients
Standard Error
Intercept
80.390
3.102
X
-2.137
0.248
a.
Perform a t test and determine whether or not demand and unit price are related. Let =
0.05.
b.
Perform an F test and determine whether or not demand and unit price are related. Let =
0.05.
c.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.
d.
Compute the coefficient of correlation and explain the relationship between demand and unit
price.
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Regression
0.000
Residual
Total
Intercept
X
indicating that as unit price increases demand decreases.
30. Shown below is a portion of a computer output for a regression analysis relating supply (Y in
thousands of units) and unit price (X in thousands of dollars).
ANOVA
df
SS
Regression
1
354.689
Residual
39
7035.262
Coefficients
Standard Error
Intercept
54.076
2.358
X
0.029
0.021
a.
What has been the sample size for this problem?
b.
Perform a t test and determine whether or not supply and unit price are related. Let = 0.05.
c.
Perform and F test and determine whether or not supply and unit price are related. Let =
0.05.
d.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.
e.
Compute the coefficient of correlation and explain the relationship between supply and unit
price.
f.
Predict the supply (in units) when the unit price is $50,000.
