# Regression Problems

1. In order to asses the profitability of additional hours spent on various projects, a manager decided to regress profitability of the project (Profits) vs. the number of hours spent on developing a project (Time). Profits are expressed in thousands of dollars. The results of the regressions are given below:

Regression: Profits

Constant Time

Coefficient 3.35738712 1.8163041

Std error of coef 1.965806 0.3640728

t-ratio 1.7079 4.9888

p-value 13.1412% 0.1585%

beta-weight 0.8835

std error of regression 2.81544425

R-squared 78.05%

Adjusted R-squared 74.91%

Number of observations 9

Residual degrees of freedom 7

t-statistic for computing

95% confidence intervals 2.3646

a. write the regression equation

b. how much does the average profit from a project increase when the team spends one more hour on a project?

c. Using α = 0.10 can you reject the null hypothesis that the true value of the constant in the regression model is not zero? Explain.

d. Using α = 0.05 can you reject the null hypothesis that the true value of the coefficient of the Time variable is not zero? Explain

e. If the team will work 100 hours on a project what will be the expected or mean profit from the project?

f. Write a hypothesis to test the claim that each extra hour spent working on the project increases profitability of that project by less than $250.

2.

Regression: Profits

Constant Energy cost

Coefficient 300.156701 17.14956955

Std error of coef 290.462959 6.075477932

t-ratio 1.0334 2.8228

p-value 30.7795% 0.7458%

beta-weight 0.4119

std error of regression 392.6116924

R-squared 16.96%

Adjusted R-squared 14.84%

Number of observations 41

Residual degrees of freedom 39

t-statistic for computing

95% confidence intervals 2.0227

a. Given this output, what is an estimate for the change in price of a refrigerator model when its annual energy costs decrease by $20?

b. Given this estimate, would you go ahead with the new technology? Explain.

c. Does this estimate make sense? Explain.

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1. In order to asses the profitability of additional hours spent on various projects, a manager decided to regress profitability of the project (Profits) vs. the number of hours spent on developing a project (Time). Profits are expressed in thousands of dollars. The results of the regressions are given below:

Regression: Profits

Constant Time

Coefficient 3.35738712 1.8163041

Std error of coef 1.965806 0.3640728

t-ratio 1.7079 4.9888

p-value 13.1412% 0.1585%

beta-weight 0.8835

std error of regression 2.81544425

R-squared 78.05%

Adjusted R-squared 74.91%

Number of observations 9

Residual degrees of freedom 7

t-statistic for computing

95% confidence intervals 2.3646

a. write the regression equation

b. how much does the average profit from a project increase when the team spends one more hour on a project?

c. Using α = 0.10 can you reject the null hypothesis that the true value of the constant in the regression model is not zero? Explain.

d. Using α = 0.05 can you reject the null hypothesis that the true value of the coefficient of the Time variable is not zero? Explain

e. If the team will work ...

#### Solution Summary

The solution gives detailed interpretation of multiple regression analysis results. Significance of regression coefficients, R square value, slope are discussed in the solution.