Question

Price	Rooms	Neighborhood
309.6	7	0
307.4	8	0
340.3	9	0
346.5	12	0
298.2	6	0
337.8	9	0
324.1	10	0
313.2	8	0
327.8	9	0
325.3	8	0
308.5	6	1
381.3	13	1
337.4	10	1
346.2	10	1
342.4	9	1
323.7	8	1
329.6	8	1
343.6	9	1
360.7	11	1
348.3	9	1

1. Predict the selling price for a house with nine rooms that is located in the east-side neighborhood. Construct a 95% confidence interval estimate and 95% prediction interval.
2. Perform a residual analysis on the results and determine whether the regression assumptions are valid.
3. Is there a significant relationship between selling price and the two independent variables (rooms and neighborhood) at the 0.05 level of significance?
4. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.
5. Construct and interpret a 95% confidence interval estimate of the population slope for the relationship between selling price and number of rooms.
6. Construct and interpret a 95% confidence interval estimate of the population slope for the relationship between selling price and neighborhood.
7. Compute and interpret the adjusted r².
8. (omit…)
1. What assumption do you need to make about the slope of selling price with number of rooms.
10. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.
11. On the basis of the results of (f) and (l), which model is most appropriate? Explain.

Answer 1

[The variable "Neighborhood" has not been properly defined. I am assuming that Neighborhood = 1 for East-side.]

(a)

	R²	0.867
	Adjusted R²	0.851	n	20
	R	0.931	k	2
	Std. Error	7.739	Dep. Var.	Price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	6,635.4808	2	3,317.7404	55.39	3.58E-08
Residual	1,018.2487	17	59.8970
Total	7,653.7295	19
Regression output					confidence interval
variables	coefficients	std. error	t (df=17)	p-value	95% lower	95% upper	std. coeff.
Intercept	243.7371						0.000
Rooms	9.2189	1.0296	8.954	7.62E-08	7.0466	11.3913	0.809
Neighborhood	12.6967	3.5354	3.591	.0023	5.2378	20.1557	0.325

Predicted values for: Price
			95% Confidence Interval		95% Prediction Interval
Rooms	Neighborhood	Predicted	lower	upper	lower	upper	Leverage
9	1	339.4043	334.1998	344.6088	322.2664	356.5422	0.102

Predicted price when Rooms = 9 and Neighborhood = 1 is 339.4043

The 95% confidence interval is [334.1998, 344.6088]

The 95% prediction interval is [322.2664, 356.5422]

(b)

The residuals show a linear trend so the normality condition is valid.

(c)

The global p- values as well as the p- values for the two independent variables separately are < 0.05. So, there a significant relationship between selling price and the two independent variables (rooms and neighborhood) at the 0.05 level of significance.

(d)

Yes, bot independent variables are significant in this regression, so both should be retained.

The best-fit model equation is Price = 243.7371 + 9.2189 Rooms + 12.6967 Neighborhood.