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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%
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.


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.

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.