# ISyE 6414 Homework 2 solution

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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.