Question

In: Statistics and Probability

A publisher of college textbooks conducted a study to relate profit per text y to cost...

A publisher of college textbooks conducted a study to relate profit per text y to cost of sales x over a 6-year period when its sales force (and sales costs) were growing rapidly.  These inflation-adjusted data (in thousands of dollars) were collected:

x  = {5.0, 5.6, 6.1, 6.8, 7.4, 8.6}                y = {16.5, 22.4, 24.9, 28.8, 31.5, 35.8}

1. It is a multiple choice question.

The regression model is..

A. E(y) + ε

B. y= B0+ B1x

C. y= B0 + B1x + ε

D. None of these

2. Interpet r 2

3. Construct a 95% CI for Beta one

Solutions

Expert Solution

X Y X * Y
5 16.5 82.5 25 272.25
5.6 22.4 125.44 31.36 501.76
6.1 24.9 151.89 37.21 620.01
6.8 28.8 195.84 46.24 829.44
7.4 31.5 233.1 54.76 992.25
8.6 35.8 307.88 73.96 1281.64
Total 39.5 159.9 1096.65 268.53 4497.35

Equation of regression line is


b = 5.1806


a =( 159.9 - ( 5.1806 * 39.5 ) ) / 6
a = -7.4559
Equation of regression line becomes

Part 1)  

The regression model is   y= B0 + B1x + ε

Part 2)

Part 3)

X Y Sxx Syy Sxy
5 16.5 2.506839 103.0225 16.0705 25
5.6 22.4 0.966879 18.0625 4.179025 31.36
6.1 24.9 0.233579 3.0625 0.845775 37.21
6.8 28.8 0.046959 4.6225 0.465905 46.24
7.4 31.5 0.666999 23.5225 3.960995 54.76
8.6 35.8 4.067079 83.7225 18.45281 73.96
Total 39.5 159.9 8.488333 236.015 43.975 268.53

Confidence Interval



95% confidence interval is



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