Question

Price (in K)	Sqft
310.0	2650
313.0	2600
320.0	2664
320.0	2921
304.9	2580
295.0	2580
285.0	2774
261.0	1920
250.0	2150
249.9	1710
242.5	1837
232.0	1880
230.0	2150
228.5	1894
222.0	1928
223.0	1830
220.5	1767
216.0	1630
218.9	1680
204.5	1725
204.5	1500
202.5	1430
202.5	1360
195.0	1400
201.0	1573
191.0	1385
274.5	2931
260.3	2200
230.0	2277
235.0	2000
207.0	1478
207.0	1713
197.2	1326
197.5	1050
194.9	1464
190.0	1190
192.6	1156
194.0	1746
192.0	1280
175.0	1215
177.0	1121
177.0	1050
179.9	1733
178.1	1299
177.5	1140
172.0	1181
320.0	2848
264.9	2440
240.0	2253
234.9	2743
230.0	2180
228.9	1706
225.0	1948
217.5	1710
215.0	1657
213.0	2200
210.0	1680
209.9	1900
200.5	1565
198.4	1543
192.5	1173
193.9	1549
190.5	1900
188.5	1560
186.0	1365
185.5	1258
184.9	1314
180.0	1338
180.9	997
180.5	1275
180.0	1030
178.0	1027
177.9	1007
176.0	1083
182.3	1320
174.0	1348
172.0	1350
166.9	837
234.5	3750
202.5	1500
198.9	1428
187.0	1375
183.0	1080
182.0	900
175.0	1505
167.0	1480
159.0	1142
212.0	1464
315.0	2116
177.5	1280
171.0	1159
165.0	1198
163.0	1051
289.4	2250
263.0	2563
174.9	1400
238.0	1850
221.0	1720
215.9	1740
217.9	1700
210.0	1620
209.5	1630
210.0	1920
207.0	1606
205.0	1535
208.0	1540
202.5	1739
200.0	1715
199.0	1305
197.0	1415
199.5	1580
192.4	1236
192.2	1229
192.0	1273
191.9	1165
181.6	1200
178.9	970

Report Write-up Structure

1. Introduce the study with a one paragraph scenario that mentions what the study is about and what the objectives are.
2. Describe the numerical dependent (i.e., response) variable of interest as well as the numerical independent (predictor) variable that will be used to develop the simple regression model. Appropriate tables, charts, and descriptive summary measures, techniques for which were reviewed in M1 should be included in the body of this section or in an Appendix to the report.
3. Create a Simple Regression Modeling: is a section, based on M2, demonstrating the complete development of a simple linear regression model using an appropriate numerical predictor variable. An appropriate value of the predictor variable should be used to obtain the prediction (i.e. the value of the dependent/response variable), along with the confidence interval estimate for the mean response Appropriate tables and charts should be included in the body of this section or in an Appendix to the report.
4. Summary of Findings: The report should end with a short paragraph that connects to the Introduction section scenario.

Extra data: Random sample of 117 homes for resale

Answer 1

Solution:

Here, we have to use the regression model or least squares regression equation for the prediction of the dependent variable or response variable as price of the home (in k) based on the independent variable or explanatory variable area of the home (in sq.ft.). The required regression model by using the excel data analysis is given as below:

Regression Statistics
Multiple R	0.844795099
R Square	0.713678759
Adjusted R Square	0.711189009
Standard Error	20.44511654
Observations	117
ANOVA
	df	SS	MS	F	Significance F
Regression	1	119819.147	119819.147	286.6467637	5.14635E-33
Residual	115	48070.32087	418.0027901
Total	116	167889.4679
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	109.7819307	6.285481916	17.46595283	3.87682E-34	97.33160109	122.2322602
Sqft	0.061366681	0.003624592	16.9306457	5.14635E-33	0.054187062	0.0685463

From above regression output, it is observed that the correlation coefficient between the dependent variable or response variable price of the home (in k) and the independent variable or explanatory variable area of the home (in sq.ft.) is given as 0.8448 approximately. This means there is a strong positive linear association or relationship or correlation exists between the given two variables price of the home and area of the home. The value of the R square or the coefficient of determination is given as 0.7137 approximately, which means about 71.37% of the variation in the dependent variable price of the home is explained by the independent variable area of the home.

The p-value for this regression model is given as 0.00 approximately which is less than the alpha value of 0.05 or the 5% level of significance, so we reject the null hypothesis. There is sufficient evidence to conclude that the given regression model is statistically significant and we can use this regression model for the prediction of the dependent variable price of the home based on the independent variable area of the home.

The slope and intercept of the regression equation are statistically significant as their corresponding p-values are approximately equal to 0.00.

The regression equation for the prediction of dependent variable price of the home is given as below:

y = 109.7819 + 0.0614*x

Price (in k) = 109.7819 + 0.0614*area (in sq.ft.)