Question

If i can have the chart filled out with work for my understanding. I would greatly appreciate it.

An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the data below.

Apartment         Monthly Rent ($)       Size (Sq. Feet)

       1                           950                               850

       2                        1,600                            1,450

       3                        1,200                            1,085

       4                        1,500                            1,232

       5                           950                               718

       6                        1,700                            1,485

       7                        1,650                            1,136

       8                           935                               726

       9                           875                               700

     10                       1,150                               956

     11                        1,400                            1,100

     12                        1,650                            1,285

     13                        2,300                            1,985

     14                        1,800                            1,369

     15                        1,400                            1,175

     16                        1,450                            1,225

     17                        1,100                            1,245

     18                        1,700                            1,259

     19                        1,200                            1,150

     20                        1,150                               896

     21                        1,600                            1,361

     22                        1,650                            1,040

     23                        1,200                               755

     24                           800                            1,000

     25                        1,750                            1,200

Excel output for this problem is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.850061
R Square	0.722603
Adjusted R Square	0.710543
Standard Error	194.5954
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2268777	2268777	59.91376	7.52E-08
Residual	23	870949.5	37867.37
Total	24	3139726

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	177.1208	161.0043	1.1001	0.28267	-155.941	510.1831	-155.941	510.1831
Size	1.065144	0.137608	7.740398	7.52E-08	0.78048	1.349808	0.78048	1.349808

4. At the 0.05 level of significance, is there evidence of a linear relationship between the size of the apartment and the monthly rent? Answer using the Excel output given above.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.850061
R Square	0.722603
Adjusted R Square	0.710543
Standard Error	194.5954
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2268777	2268777	59.91376	7.52E-08
Residual	23	870949.5	37867.37
Total	24	3139726

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	177.1208	161.0043	1.1001	0.28267	-155.941	510.1831	-155.941	510.1831
Size	1.065144	0.137608	7.740398	7.52E-08	0.78048	1.349808	0.78048	1.349808

4. At the 0.05 level of significance, is there evidence of a linear relationship between the size of the apartment and the monthly rent? Answer using the Excel output given above.

Ans: Here p value of size is 0.0000 Since the p value is less than 0.05 we can say that there is linear relationship between the size of apartment and monthly rent.

Note:If p value is less than alpha then there is a linear relationship between two variables.

Please do the comment for any doubt or clarrification.