1. Use the following Minitab output to determine the best-fitting regression equation for these data
2. What percentage of the total variation in the number of rush returns(y) is explained by this equation?
3. For this year, the economic index (x1) is 169, the population within 1 mile of the office (x2) is 10,212, and the average income in Ithaca (x3) is 26,925. How many rush returns should Pam expect to process?
Pam Schneider owns and operates an accounting firm in Ithaca, New York. Pam feels that it would be useful to be able to predict in advance the number of rush income-tax returns during the busy March 1 to April 15 periods so that she can better plan her personnel needs during this time. She has hypothesized that several factors may be useful in her prediction. Data for these factors and number of rush a return for past years are as follows:
X1 X2 X3 y[Number of rush
[Economic [Population within 1 [Average Income Returns, March 1 to April 15]
Index] mile of office] In Ithaca]
99 10188 21465 2306
106 8566 22228 1266
100 10557 27665 1422
129 10219 25200 1721
179 9662 26300 2544
a) Use the following Minitab output to determine the best-fitting regression equation for these data:
The regression equation is
Y = -1275 + 17.1 x1 + 0.541 x2 - 0.174x3
Predictor Coef Stdev t-ratio p
Constant -1275 2699 -0.47 0.719
x1 17.059 6.908 2.47 0.245
x2 0.5406 0.3144 1.72 0.335
x3 -0.1743 0.1005 -1.73 0.333
s = 396.1 R-sq = 87.2%
b) What percentage of the total variation in the number of rush returns(y) is explained by this equation?
c) For this year, the economic index (x1) is 169, the population within 1 mile of the office (x2) is 10,212, and the average income in Ithaca (x3) is 26,925. How many rush returns should Pam expect to process?