What proportion of the total variation in the production of car tires is accounted for by the set of independent variables?

Excel Question

1. The production of car tires in any given year is related to the number of cars produced

that year and in prior years. Suppose our econometric model resulted in the following

data.

Regression Coefficient t-stat

X1=Cars produced this year 5.00 10.4

X2=Cars produced last year 0.25 0.6

X3=Cars produced 2 years ago 0.67 1.4

X4=Cars produced 3 years ago 2.12 2.7

X5=Cars produced 4 years ago 3.44 6.5

Constant -50,000

Multiple R 0.83

1. Write out the regression equation.
2. Which independent variable has the most significant effect on the production of car

tires?

1. What proportion of the total variation in the production of car tires is accounted for by the set of independent variables?

2. A multiple regression analysis showed the following ANOVA table result.

Based on the information in the ANOVA,

1. How many independent variables were included in the multiple regression analysis?
2. What is the multiple coefficient of determination expressed as a percent?
3. What is the decision regarding the global null hypothesis, at 0.05 significance level?
4. A sociologist claims that the success of students in college (measured by their GPA) is related to their family’s income. For a sample of 25 students, the correlation coefficient is 0.6. Using the 0.01 significance level, can we conclude that there is a positive correlation between the variables?

4. In a study of several companies going public for the first time, a researcher is particularly interested in the relationship between the size of the offering and the pric per share. A sample of 15 companies that recently went public revealed the following information.

IS 601

Company Size ($ millions)

x

Price per Share

y

1 9.0 10.8

2 94.4 11.3

3 27.3 11.2

4 179.2 11.1

5 71.9 11.1

6 97.9 11.2

7 93.5 11.0

8 70.0 10.7

9 160.7 11.3

10 96.5 10.6

11 83.0 10.5

12 23.5 10.3

13 58.7 10.7

14 93.8 11.0

15 34.4 10.8

Use a software to:

1. Determine the regression equation.
2. Conduct a test to determine whether size is a significant variable in describing the price per share. (use alpha 0.05)

1. Determine the coefficient of determination. Do you think the researcher should be satisfied with using the size of the offering as the independent variable?

Include a copy of your software analysis.