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Linear regression - Confidence interval, prediction interval

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Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.

x= 26,27,33,29,29,34,30,40,22
y= 290,305,325,327,356,411,488,554,246
Now we want to build the linear regression model,

*With the information provided above please answer the followin questions:
1. Do the data suggest that size is useful as a predictor if price for custom homes in the Equestrain Estates? Perform the required hypothesis at the 0.01 level of significance.

2. a. Find a 99% confidence interval for the slope of the population regression line that relates price to size for custom homes in the Equestraion Estates.

b. Interpret your answer to part (a).

3. a. Determine a point estimate for the mean price of all 2800-sq-ft Equestrain Estates home.

b. Find 99% confidence interval for the mean price of all 2800-sq-ft Equestrain Estate.

c. Find the predicted price of a 2800-sq-ft Equestrain Estate home.

d. Determine a 99% prediction interval for the price of a 2800-sq-ft Equestrain Estate home.

4. At the 0.5% significance level, do the data provide sufficiant evidence to conclude that, for custom homes in the Equestrain Estates, size and price are positively linearly correlated?

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Solution Preview

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Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand
X Y X^2
26 290 676
27 305 729
33 325 1089
29 327 841
29 356 841
34 411 1156
30 488 900
40 554 1600
22 246 484
30 366.8888889 Average
8316 Total
Run regression on the data. Go to tools, data analysis and regression.
The regression output is below

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.828731691
R Square 0.686796216