Question

The following data relate fat content (X) and calories (Y) for a sample of hamburgers. Find the correlation coefficient and the intercept and slope of the least squares line.

## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## x 19 31 34 35 39 39 43
## y 410 580 590 570 640 680 660

1. Attach a plot of the data

2. Compute the intercept and the slope of the least squares line

b0 = ____________ ; b1 = ____________

3. Compute 95% confidence intervals for 0 and 1, the intercept and slope of the true regression line, also give the value of t you used

0: _______ _______ ; 1: _______ _______ ; t = ______

4. Give the following:

R2 = _______________ ; Radj2 = _______________

6. What would you estimate as the calory count of a hamburger with fat content

x = 30: y^ = _____________ ; x = 40: y^ = _____________

7. The simple linear models says y=0+1x+, where Var(y)=Var()=2. For the data in this problem, what is your estimate of this variance?

^2 = _____________

8. Give a 95% confidence interval for the mean calorie content of hamburgers with x = 32 and a 95% prediction interval for the calorie content of a hamburger with x = 38

x=32, CI: _______ _______ ; x=38, PI: _______ _______

Answer 1

Analysis is performed using minitab

a)

to plot data with  least squares line

commands in minitab are given in the screenshot

Plot data with  least squares line

b0 = 211 ; b1 = 11.06

Compute 95% confidence intervals for 0 and 1, the intercept and slope of the true regression line, also give the value of t you used

95% confidence interval for intercept = (82.1640,339.7437)

value of t =4.2105

95% confidence interval for slope = (7.3799,14.7311)

value of t =7.7317

Give the following:

R2 = 0.92 ; Radj2 = 0.91

What would you estimate as the calory count of a hamburger with fat content

x = 30:

The regression equation is
y = 211.0 + 11.06 x

y = 211.0 + 11.06*30

y = 542.8

x = 40:

y = 211.0 + 11.06 x

y = 211.0 + 11.06*40

y = 653.4

estimate of this variance?

S^2 = (27.33)^2

S^2 =746.9289