Now consider an alternative model to that above In (HOMES)-A+ 2 IRATE Estimation
ID: 3340560 • Letter: N
Question
Now consider an alternative model to that above In (HOMES)-A+ 2 IRATE Estimation results (from gretl): Model 2: OLS, using observations 1992:01-2010:03 (T-219) Dependent variable: I homes coefficient sd.error -ratio p-value const 6.69617 0.147416 45.42 8.28e-113 rate 0,00430059 0.0211150.2037 0.8388 Mean dependent var 6666473 S.D. dependent var 0.325283 Sum squared resid 23.06191 S.E. of regression R-squared 0000191 0.326000 yhat2 predicted (fitted) values from this regression predy exp (yhat2) Correlation coefficients, using the observations 1992.01-201003 5% critical value (two-tailed)-0. 1326 for n-219 predy 01667 homes 1.0000 yhat2 0000 predy 0.1677 1.0000 10000 iv In this model, what are the natural and corrected predictions for home sales when the interest rate is 5% (irate-5)? which would you choose for your point prediction? Construct a 95% confidence interval for your prediction in part iv. (Hint: Observation 2009-03 has irate-5. See below) v. For 95% confidence intervals, 1(217, 0025)-1971 1 homes prediction std enor 95% interval 1992:0 6516193 6.659912 0.328327 6012793-7.307030 200903 5.805135 6674663 0.329208 vi. What is the generalized R for this model? Comparing to the R2 from part ii, which model would you choose based on goodness-of-fit?Explanation / Answer
Here dependent variable is homes and independent variable is interest rate.
We have given the regression output.
The regression equation is,
ln (homes) = 6.696 - 0.0043*irate
Intercept = 6.696
Slope= -0.0043
Interpretation of slope : For one unit change in interest rates will be 0.0043 unit decrease in natural logarithm of homes.
iv) Now we have to predict homes when irates =5
ln (homes) = 6.696 - 0.0043*5 = 6.6745
v) Here we have to find 95% confidence interval for B is (6.63, 6.72).
vi) R-sq = 0.000191
It expresese the proportion of variation in response variable which is expressed by variation in independent variable.
Now we see that interest rate is insignificant variable because P-value for irate is 0.8388.
P-value > alpha
Therefore irate is insignificant variable.
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