The regession model output of an autoregressive (AR2) model are shown below: Coefficients Constant 0.006503139 Lag 1 Lag 2 1.089593514 -0.09525277 Assume Lag 1 and Lag 2 are 1.0920 and 1.0910, respectively. The predicted value of the y-variable is closest to 1.0895 O .0065 O 1.08927 1.09242
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- The table shows a part of an output of a linear regression model predicting the average fare on different flight routes. Data Table Regression Table Coefficient Constant 95.80976147 COUPON −9.61654124 DISTANCE 0.080733811 PAX −0.000167343 What is the difference in prediction of the following two routes? Route A that is 3,000 miles, with COUPON=1.5 and PAX=6,000 Route B that is 3,000 miles, with COUPON=1.2 and PAX=6,000.Consider the least square estimate and the ridge regression estimate of the linear regression coefficients, which of the following(s) is (are) always correct? and why? A. Least square has a smaller training error. B. Ridge regression has a smaller training error. C. Least square has a smaller test error. D. Ridge regression has a smaller test error.A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920 Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
- A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920 Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance.Consider an estimated linear regression model with a response Y and 4 predictors X1, X2, X3, X4. For a random sample of 25 observations on the response and the 4 predictors, the following estimates are obtained using Excel. Regression Statistics Multiple R 0.859825564 Standard Error 127.606 What is the adjusted R-square of the fitted model?A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and addition to savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920a. Write out the estimated regression equation for the relationship between the variables. b. Compute the coefficient of determination. What can you say about the strength of thisrelationship? c. Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance. d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
- The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 Analysis of Variance 0.0000 Source DF SS MS F p Regression 3 413.1291 138.7097 *** 0.00 Error 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equationThe regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 Analysis of Variance 0.0000 Source DF SS MS F p Regression 3 413.1291 138.7097 *** 0.00 Error 50 457.7607 2.2888 Total 53 c) Fill in the missing values ‘*’, ‘**’, and ‘***’. d) Hence test whether ? is significant. Give reasons for your answer.The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 Analysis of Variance 0.0000 Source DF SS MS F p Regression 3 413.1291 138.7097 *** 0.00 Error 50 457.7607 2.2888 Total 53 e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
- Suppose that a multiple linear regression model was fit to data and that the following output resulted: Coefficients: (Intercept)exam1exam2attendance Estimate20.001.3002.5000.685 Std. Error4.2910.2610.2745.608 t value-4.6604.9819.124 0.122 Pr(>|t|)<0.0001<0.0001<0.00010.9032 Perform a backwards selection process. Select the variable that would be removed first from the model. The significance level is 0.05 for testing purposes. attendance exam2 exam1A. Identify the regression analyses necessary for testing this initial model. B. What are the direct and indirect effects of z2 on z5?For the regression model Yi = b0 + eI, derive the least squares estimator.