25 pts 5. The National Association of Realtors has reported data on housing affo
ID: 3297592 • Letter: 2
Question
25 pts 5. The National Association of Realtors has reported data on housing affordability. The following data shows the affordability index, defined as the average monthly mortgage payment as a percentage median household income, and the cost of the mortgage as the average mortgage rate ten years. of in percent for Year Payment% Rate% 22.0 21.4 19.3 18.1 18.5 18.9 18.8 18.7 17.4 18.0 5.5 4.76 3.57 2.62 2.93 3.31 3.17 3.14 2.56 2.79 10 Determine the least square regression line for estimating housing affordability based on average mortgage rate. a.Explanation / Answer
MTB > Name c4 "CLIM1" c5 "CLIM2" c6 "PLIM1" c7 "PLIM2"
MTB > Regress 'Payment' 1 'Rate';
SUBC> Constant;
SUBC> Predict 6;
SUBC> CLimits 'CLIM1'-'CLIM2';
SUBC> PLimits 'PLIM1'-'PLIM2';
SUBC> Brief 1.
a]
Regression Analysis: Payment% versus Rate%
The regression equation is : Payment% = 13.9 + 1.52% Rate
Predictor Coef SE Coef T P
Constant 13.9026 0.2711 51.27 0.000
Rate 1.51597 0.07629 19.87 0.000
S = 0.219955 R-Sq = 98.0% R-Sq(adj) = 97.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 19.102 19.102 394.83 0.000
Residual Error 8 0.387 0.048
Total 9 19.489
b]
Predicted Values for New Observations as interest rate is 6%
New Obs Fit SE Fit 95% CI 95% PI
1 22.9985 0.2077 (22.5195, 23.4774) (22.3009, 23.6961)
c]
here R2 = 98.0% it is also called as coefficient of determinstion and there is 98% variation is explained in housing affordability to interest rate.
d]
P-value = 0.000 is less than the given level of signofocane 0.05. Hence we reject the null hypothesis. That is reject slope = 0.
Conclusion:
At 5% level of signofocane, the slope of the regression equation is differs significantly from 0.
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