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Regression Analysis: Penrose Consulting Company

The Penrose Consulting Company performs studies for universities that want to raise money through their alumni associations. As part of its work, it recently sampled 18 universities across the United States and determined the number of alumni contacts and the total dollars in gifts received from those alumni during the previous academic year. Here are the data:

School Alumni Money Received
1 987 234700
2 1350 769000
3 2345 1230000
4 1300 450780
5 12569 6450000
6 8560 2650000
7 3450 1430000
8 1890 230000
9 23456 4560000
10 12700 2678900
11 4600 800000
12 5700 2780000
13 23600 7.00E+06
14 33450 8900000
15 28900 8600000
16 1800 133000
17 12800 5790000
18 20540 2400300

a) Draw a scatter plot of these two variables. Based on this plot only, does it appear that a linear relationship exists between the two variables?

b) Compute the correlation coefficient and discuss what it measures.

c) Test to determine whether the population correlation coefficient is actually 0, using an alpha level of 0.05.

d) Compute the least squares regression equation using money collected as the dependent variable and number of alumni contacted as the independent variable. For this model, compute, and interpret, the following:

1) R-square
2) Standard error of the estimate
3) 90% confidence interval estimate for the true slope coefficient
4) 95% prediction interval for the money collected for a particular university given that 4,000 alumni are contacted
5) Referring to part d, conduct the appropriate hypothesis test to determine whether the overall regression model explains a significant portion of the variation in the dependent variable. Use a significance level of 0.05 to conduct the test.

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