Gru noticed that virtually all of his Minions wear goggles.They actually have poor eyesight (they are typically nearsighted)without their goggles. Out of concern for his Minions, he decidesto investigate the eyesight of his Minions as they age. He gathersa random sample of Minions and records their prescription (measuredin diopters) and their age in years. He constructs a linear modeland gets the following computer outputs.

Scatterplot of Minion Glasses Prescription vsAge

11.522.530.511.52Age (years)Prescription (diopters)

Residual Plot

11.522.530.10.20.30.40.5-0.1-0.2-0.3-0.4-0.5Age(years)Residual

Coefficients:

	Estimate	Std Err	t-value	p-value
(Intercept)	0.2506	0.124	2.0208	0.05623
Age	0.4556	0.0616	7.3904	2.86 E -7

Residual standard error: 0.1761 on 21degrees of freedom
r2r2= 0.7223,
F-statistic: 54.6173 on 1 and 21 DF,p-value: 2.86 E -7

a) Using the provided information above, does a linear modelseem appropriate for Gru's data? Your response should include someform of an analysis as discussed in class such as hypothesistesting, discussion of provided graphs, etc...

b) Write the slope of the linear model.

Slope:

Interprete the slope in context.

c) Determine the correlation coefficient of Gru's model:

Based on the magnitude, interpret the correlationcoefficient.

d) Write out the equation of linear regression in the form y =b0 + b1x.

e) One of the points on the scatterplot is (2.5,1.8). Calculatethe residual for this point.

f) State the value of coefficient ofdetermination r2 and explain it in context.