Real-estate agents are often interested in the factors that predict the selling prices of houses. To study the relationship between the size of a house and the selling price, an agent collected data on 42 houses and obtained the following variables:

Y = Selling price of the house (in hundreds of thousands)

X = The size of the house (in square meters).

A simple regression model of the form:

Price = b₀ + b₁Size + e

was estimated and an excerpt from the output is shown below.

Regression Statistics
Multiple R	0.6942319
R Square	0.4819579
Adjusted R Square	0.4690069
Standard Error	58.263857
Observations	42
ANOVA
	df	SS	MS	F
Regression	1	126328.8571	126328.9	37.21381
Residual	40	135787.0791	3394.677
Total	41	262115.9362
	Coefficients	Standard Error	t Stat	P-value
Intercept	279.38	37.983	7.3553	0.0000
Size	0.7562	0.1240	6.1003	0.0000

Answer the following questions, using the above information.

i. Determine the dependent and independent variable of the model.

Dependent variable:

Independent variable:

ii. Based on the estimation results in the output, write down the estimated regression model in the form: Price^ = + Size

Price^ =

iii. Interpret the estimated intercept term ( ):

Interpret the estimated slope coefficient ( ).

iv. Using the p-value from the output, test at the 5% significance level that house size (X) has a significantly positive effect on the price.

H_o:

H_A:

Test statistic and its sampling distribution:

Level of significance a =

Decision rule (p-value method):

p-value:

Conclusion:

v. Value of the coefficient of determination R² =

Interpret the value of R² and comment on the fitness of the model.

vi. What is the standard error of estimate (s_e)? Using the standard error of estimate, assess the fitness of the model.

vii. Forecast the selling price of a house that is 240 square meters

viii. Suppose the correlation coefficient is 0.694. Comment on the strength and direction of the linear relationship between the two variables.

ix. Test the hypothesis that the population coefficient of correlation (r) is significantly different from zero (r ¹ 0).

H_o:

H_A:

Test statistic and its distribution:

Level of significance a =

Decision rule:

Calculate the value of the test statistic or p-value:

Conclusion:

Price 700 600 500 400 300 200 y = 0.7562x+279.38 100 50 100 150 200 250 300 350 400 450 House Size (m^2) House Price ($000s)