Question

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

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

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