Question

A table of house pricing data is linked below. Use software to do further analyses with the multiple regression model of y=selling price of home in​ thousands, x1=size of​ home, and x2=number of bedrooms. Then use this model to complete parts a through c below.

Data:

y_Price_($)   x1_Size_(sq_ft)   x2_Bedrooms
309900   3179   5
161700   1738   3
162100   1901   2
132100   996   1
210900   1676   2
170100   1662   2
189700   1396   2
286100   3627   4
304700   3961   5
252700   3395   5
120200   795   1
286600   3475   4
167800   1416   2
118200   1041   1
260900   2763   4

b. Report and interpret the t statistic and​ P-value for testing H_0​: β₂ = 0 against H_a​: β₂ > 0.

t = 1.093

c. Report the p-value corresponding to this t statistic.

P-value = ____ (round to four decimal places as needed)

Answer 1

The analysis after feeding the data in MS Excel is presented here

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.951938473
R Square	0.906186856
Adjusted R Square	0.890551332
Standard Error	22710.89266
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	2	59786581586	2.99E+10	57.95692262	6.81683E-07
Residual	12	6189415747	5.16E+08
Total	14	65975997333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	77122.51954	13691.46539	5.63289	0.000110228	47291.3791	106953.7	47291.38	106953.7
x1	41.68216976	17.80075999	2.341595	0.037277509	2.897645519	80.46669	2.897646	80.46669
x2	13964.54138	12781.74436	1.092538	0.296045333	-13884.48722	41813.57	-13884.5	41813.57

It can be seen that value of t statistic is 1.0925 and p value is 0.2960 (shown in bold above)