Question

Suppose you wish to see if there is a relationship between the price (in $100) and rating (in points) of 7 laptop computers tested by Consumer Reports. You collected the information below.

SSxx=42.2143

SSxy=76.4286

MSE=10.8968

Q1: Using the F table, find the p-value for Global Fstat.

? < p-value < ?

Q2: Find the 98% CI for β1 (with appropriate units).

What is Left Endpoint= ?

What is Right Endpoint= ?

What are the appropriate units (options dollars/point, points/dollar, points, or dollars)?

please show me how to work through this problem to get the answers.

Answer 1

Here we have n=7

The number of predictors variables is k = 1

So

dfre egression

an-1-1-7-2-5

$SSE=MSE\cdot df_{residual}=10.8968\cdot 5=54.484$

$SSR=\frac{S^{2}_{xy}}{S_{xx}}=\frac{76.4286^{2}}{42.2143}=138.3733$

So

$MSR=\frac{SSR}{df_{regression}}=138.3733$

The F test statistics is

$F=\frac{MSR}{MSE}=12.699$

The p-value is

0.010 < p-value < 0.025

Question 2:

$b_{1}=\frac{S_{xy}}{S_{xx}}=\frac{76.4286}{42.2143}=1.8105$

$se=\sqrt{MSE}=3.3010$

The standard error of slope is

$s_{b_{1}}=\frac{se}{\sqrt{S_{xx}}}=0.5081$

For 98% confidence interval critical value of t is .3.3649. So required confidence interval is

$b_{1}\pm t_{c}s_{b_{1}}=1.8105\pm 3.3649\cdot 0.5081=1.8105\pm 1.7097=(0.1008,3.5202)$

Unit : dollars / Point