Question

1. Hanna Properties specializes in custom-home resales in Equestrian Estates, an exclusive subdivision in Phoenix, AZ.  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

1. Give the simple linear regression model and assumptions.

2. Write down the least squares regression line (3 decimal places).  

3. Give the 95% confidence interval for the slope parameter.

4. Test for a significant linear relationship between x and y at the 5% significance level.  Give the hypotheses, test statistic, conclusion, and interpretation.

Answer 1

a) The simple linear regression model is , where is the error term and follows a Normal(0, ).

The assumptions are i) The error terms are independent.

ii) The variance of the error term remains the same.

iii) There exist a linear relationship between the two variables.

b) The least-square regression line is: Y = -109.917 + 15.894X

c) The 95% confidence interval for the slope parameter is (6.3, 25.486)

d) The hypothesis is: Ho: b=0 vs Ha: b0.

The test statistic is 3.918. P-value is 0.0058.

Conclusion: At a significance level of 5%, there is sufficient evidence to support the claim that the slope of the line is not 0.

Here I've attached the excel output