A computer software developer would like to use the number of downloads (in thou

Question

A computer software developer would like to use the number of downloads (in thousands) to predict the amount of revenue (in hundreds of dollars) he can make on the full version of the new shareware. Please answer the following questions based on the regression analysis below.

1)  Please state the regression equation.

2) What is the correct interpretation for the slope coefficient?

3) Predict the revenue when the number of downloads is 30,000.

4) What is the correct interpretation for the coefficient of determination R squared?

5) The 95% confidence interval estimate for the population slope is ______ , ______.

6) Is there sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance? Give a reason why.

Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30 ANOVA df SS MS F Significance F Regression 1 171062.9193 171062.9193 86.4759 0 Residual 28 55388.4309 1978.1582 Total 29 226451.3503 Coefficients Standard Error t Stat P-Value Lower 95% Upper 95% Intercept -95.0614 26.9183 -3.5315 0.0015 -150.2009 -39.9218 Download 3.7297 0.4011 9.2992 0 2.9082 4.5513

Explanation / Answer

1)from above : regression equation : Y=-95.0614+3.7297X

2) for every 1 thousand dowloads , increase in revenue is 3.7297 (in 100 dollars

3) for download x=30000; revenue =-95.0614+3.7297*30=16.8296 *100 $ =$1682.96

4)R2 =0.7554 represent variability in revenue which can be explained by variabilty in downloads

5)for 95% CI and (n-2=28) degrees of freedom ; t=2.0484

hence confidence interval =b1 -/+ t*satd error =2.9081 ; 4.5513

6) Yes as our confidence level does contain only above ) values ; that means test is significant at 5%

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