## Description

Part I. The attached data set was reported by an article in Technometrics on the selling

price, y, and the annual taxes, x (local, school, county) for 24 houses. By using R (or any

appropriate software you prefer), answer questions 1–5 and submit the relevant outputs.

1. Construct and submit a scatter plot of y versus x. Does a simple linear regression

model seem appropriate here?

2. Fit the simple linear regression model using the method of least squares, i.e., find

the least squares line, ˆy = βˆ

0 + βˆ

1x by using the software. Submit your solution

(output).

3. In plain English, interpret the meaning of the slope parameter β1.

4. In plain English, interpret the meaning of the intercept β0. Does it have a practical

meaning here?

5. Report the value of s; and then calculate s

2 and SSE.

Part II. Suppose that you obtained the following summary quantities to estimate the

parameters in a regression study. Assume that x and y are related according to the

simple linear regression model ˆy = βˆ

0 + βˆ

1x.

n = 14,

Xn

i=1

yi = 572,

Xn

i=1

y

2

i = 23530,

Xn

i=1

xi = 43,

Xn

i=1

x

2

i = 157.42, and Xn

i=1

xiyi = 1697.80.

Answer the following questions.

6. Calculate the least squares estimates of the slope and the intercept.

7. Estimate σ

2

. Hint: Use the following formula to calculate the sum of squared

errors:

SSE = SSyy − βˆ

1SSxy.

8. Use the equation of the fitted line to predict y at x = 3.7. Suppose that the

observed (actual) value of y = 46.1 when x = 3.7. Calculate the corresponding

residual.