Question

f. Interpret the slope coefficient for one of the dummy variables included in your regression model.

g. For the slope coefficient of the variable with the smallest slope coefficient (ignore sign, use absolute value), test to see if the “a priori” expectation from part (a) is confirmed. Use alpha = 0.05.

h. Interpret the coefficient of determination in this situation.

i. Test the explanatory power of the entire regression model. Please use alpha = 0.01.

j. For the variable with the largest estimated slope coefficient (ignore sign, use absolute value), construct a 90% confidence interval for the corresponding population slope coefficient.

k. Interpret the interval constructed in part (j).

l. What is the p-value associated with the model test in this situation?

m. Create the normal probability plot associated with your multiple regression model. Is the information displayed in the plot consistent with the associated error term assumption made in the model?

here is the regression summary

Regression Statistics
Multiple R	0.554741323
R Square	0.307737935
Adjusted R Square	0.296037732
Standard Error	30.54182977
Observations	362
ANOVA
	df	SS	MS	F	Significance F
Regression	6	147207.169	24534.5281	26.3019293	6.9183E-26
Residual	355	331145.195	932.803366
Total	361	478352.364
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	113.393156	11.4315172	9.91934437	1.245E-20	90.9111467	135.875165	90.9111467	135.875165
LOTSIZE	-1.211020711	0.32740277	-3.6988713	0.00025085	-1.8549136	-0.5671279	-1.8549136	-0.5671279
AGE	-0.24182222	0.14233746	-1.6989359	0.09020736	-0.5217529	0.03810843	-0.5217529	0.03810843
RMS	10.76999883	1.24970453	8.6180362	2.2783E-16	8.31224382	13.2277538	8.31224382	13.2277538
MOD KITCH	3.938467175	6.02621357	0.65355586	0.51382108	-7.9130996	15.790034	-7.9130996	15.790034
MOD BATH	7.070026791	6.04449449	1.16966387	0.24292097	-4.8174925	18.9575461	-4.8174925	18.9575461
AIRCON	33.00755236	6.06897927	5.43873209	1.0009E-07	21.0718796	44.9432251	21.0718796	44.9432251

Answer 1

h)
coefficient of determination = r^2
= 0.307737

it means that 30.77 % of variation in dependent variable is explained by independent variable

i)

significance F =6.9183E-26 << 0.01

hence the model is significant

j)

largest slope coefficient = 33.00755236 for AIRCON
se = 6.068979

t = 1.645 for 90 % CI
hence
90 % confidence interval
( 33.00755236 - 1.645 * 6.068979, 33.00755236 + 1.645 * 6.068979)
= (23.024081905,42.99102)

k)
we are 90 % confident that true slope lies in this CI
l)
p-value = 6.9183E-26