1. The following are
eight observations collected in a research study on the possible relationship
between an independent x and a dependent variable y.
|
Xi |
13 |
19 |
18 |
24 |
21 |
26 |
15 |
|
yi |
36 |
54 |
46 |
65 |
51 |
67 |
41 |
Develop a scatter
diagram for these data
Develop the estimated
regression equation for these data.
Use the estimated
regression equation to predict the value of y given x = 16
Please note that you
can either use the formula (12.6) and (12.6), a statistical package such as
StatTools, or the Regression program within Excel’s Data Analysis Add-in to
calculate the estimated regression
2. Given the following
output obtained from a regression analysis of the dependent variable Sales and
an independent variable Advertising
|
ANOVA |
|||
|
df |
SS |
MS |
|
|
Regression |
1 |
13489.58 |
13489.58 |
|
Residual |
15 |
45620.74 |
3041.38 |
|
Total |
16 |
59110.32 |
|
|
Coefficients |
Standard Error |
||
|
Intercept |
254.1 |
54.2 |
|
|
Advertising |
0.14 |
0.066 |
Use the p-value
approach to perform a F test for the significance of the linear relationship
between Advertising and Sales at the 0.05 level of significance
Calculate the
coefficient of determination
What percentage of the
variability of Sales can be explained by its linear relationship with
Advertising? What is the sample correlation coefficient?
What is the estimated
regression equation?
Use the critical value
approach to perform a t test for the significance of the linear relationship
between Advertising and Sales at the 0.05 level of significance
3. You may want to
refer to the description of the Regression Analysis output from Excel in the
Appendix of Chapter 12 before completing the following question.
The data in A.XLSX is
collected for building a regression model to estimate value of residential
homes in a mid-size Canadian city. Use this data to perform a simple regression
analysis between Value and Size.
Develop a scatter
diagram using Value as the dependent variable y and size as the independent.
Develop the estimated
regression equation.
Use the estimated
regression equation to predict the value of an 1850 square-foot home.
Use the critical-value
approach to perform a F test for the significance of the linear relationship
between Value and Size at the 0.05 level of significance.
What percentage of the
variability of Value of residential homes can be explained by its linear
relationship with Size?
Use the p-value
approach to perform a t test for the significance of the linear relationship
between Value and Size at the 0.05 level of significance.
4. The estimated
regression equation for a model involving two independent variables and 15
observations is:
yhat = 29.75 – 0.57X1+
2.53X2
Other statistics
produced for analysis include: .3, .5, Sb1.085, Sb2.35
Interpret b1and b2in this estimated regression equation
Predict y when X1and X2
Compute R and Ra
Comments on the
goodness of fit of the model
Compute MSR and MSE
Compute F and use it
to test whether the overall model is significant using a p-value (?.05)
Perform a t test for
the significance of ?1. Use a level of
significance of 0.05
Perform a t test for
the significance of ?2. Use a level of
significance of 0.05
5. Use data in 1A.XLSX
to complete the following. You will need to use a statistical package such as
StatTools or the Regression program within Excel’s Data Analysis Add-in to
generate the estimated regression equation and the ANOVA etc.
What is the estimated
regression equation using Value as the dependent variable and Size as well as
Number of Bedrooms as the independent variable?
Comments on the
goodness of fit of the model Using the coefficient of determination
Conduct F test to see
whether the overall model is significant. Use ?.05.
Perform a t test for
the significance of the Size variable. Use ?.05.
Perform a t test for
the significance of the Number of Bedrooms variable. Use ?.05.
Estimate the value of
a three-bedroom home that has 1850 square feet of space.
