1. What is the goodness of fit of this model ? Interpret the statistic. 2. At th
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Question
1. What is the goodness of fit of this model? Interpret the statistic.
2. At the 0.05 level, test the overall regression equation significance (Global F test) Write down 4-step. Based on the test, do you think the regression model work well to predict the house price?
3. At the 0.05 level, test the significance of partial coefficient for SqFeet . Write down 4-step. Do you think the area of the house will significantly affect house price?
4. Determine the 95% confidence interval for the population partial coefficients for Bedroom. Do you think the number of bedroom will affect the house price?
SUMMARY OUTPUT Regression Statistics Multiple R 0.718746199 R Square 0.516596099 Adjusted R Square 0.514017945 Standard Error 12125.44194 Observations 378 ANOVA df SS MS F Significance F Regression 2 58920631435 29460315718 200.3744042 6.42915E-60 Residual 375 55134878326 147026342.2 Total 377 1.14056E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 23974.1763 3636.86945 6.591981547 1.47531E-10 16822.96295 31125.38966 16822.96295 31125.38966 SqFeet (Quantitative) x1 40.0410133 2.508769054 15.9604222 3.96505E-44 35.10799522 44.97403139 35.10799522 44.97403139 Bedrooms (Quantitative) x2 -2359.944552 1316.355176 -1.79278708 0.073812805 -4948.30711 228.418006 -4948.30711 228.418006Explanation / Answer
1) t stat from the ANOVA table is the good ness of fite test of this model.
2) so if we have H0: b1 = 0 ; b2=0 and H1 : b1 not equal to 0 ; b2 not equal to 0
we have t stat value for b1 = 15.96 with p- value 3.965E-44 < 0.05 level of confidence and hence we reject the null hypothesis of b1=0
but on the other side t stat for b2 = -1.79 with p value = 0.073 > 0.05 . So we accept the null hypothesis of b2=0
So in a whole we will reject the H0: b1 = 0 ; b2=0
3) H0: b1 = 0
we have t stat value for b1 = 15.96 with p- value 3.965E-44 < 0.05 level of confidence and hence we reject the null hypothesis of b1=0
4) CI for partial coefficient of bedrrom (-4948 , 22841)
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