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# 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%

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 &#945; = 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 &#945; = 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%

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.

#### 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.

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