Question 6 The variable income (yearly) is examined in a regression setting where the predictor variable is lag (1) of income and the following output is produced. a) Write down the regression equation. (3 marks). b) Interpret the meaning of the slope. (3 marks). c) A dummy variable for gender (male=0, female=1) was added to the model. Interpret its coefficient of -0.2. (3 marks). us_change %>% model(TSLM(log(Income) ~ log(LagIncome))) %>% report() #> Series: Consumption #> Model: TSLM #> #> Residuals: #> Min 1Q Median 3Q Max #> -2.5824 -0.2778 0.0186 0.3233 1.4223 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.5445 0.0540 10.08 < 2e-16 *** #> Log(LagIncome) 1.1000 0.0467 5.82 2.4e-08 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 0.591 on 196 degrees of freedom #> Multiple R-squared: 0.147, Adjusted R-squared: 0.143 #> F-statistic: 33.8 on 1 and 196 DF, p-value: 2.4e-08
Added by James L.
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The regression equation: The regression equation is a mathematical representation of the relationship between the dependent and independent variables. From the given output, the regression equation would be: Income = 5445.0540 + 1000 * Log(LagIncome) Show more…
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For this question, use the following multiple regression output (which may differ from the output in other questions, even though the variables are the same) SUMMARY OUTPUT Regression Statistics Multiple R 0.534 R Square 0.285 Adjusted R Square 0.247 Standard Error 4791.473 Observations 100 ANOVA df SS MS F Significance F Regression 5 859571711.8 1.72E+08 7.488 5.940E-06 Residual 94 2158071843 22958211 Total 99 3017643555 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3637.638 2700.353 1.347 0.1812 -1723.976 8999.252 Annual Income ($1000) 108.876 19.008 5.728 1.216E-07 71.135 146.617 Household Size 285.883 218.539 1.308 0.1940 -148.032 719.797 Education -200.021 320.557 -0.624 0.5342 -836.494 436.451 TV Hours -3.683 28.451 -0.129 0.8973 -60.175 52.808 Age -10.82 46.632 -0.232 0.817 -103.41 81.769 Find the predicted annual charges for a 44-year old customer with an annual income of $65 (thousand), a household size of 5, 2 years of post-high school education, 32 hours of watching television per week.
Lucas F.
Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 where 0 = female and 1 = male). The following is a partial result of a computer program that was used on a sample of 20 individuals. Coefficient Standard Error X1 0.6251 0.094 X2 0.9210 0.190 X3 -0.510 0.920 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 84 Error 112 a. Compute the coefficient of determination. b. Perform a t-test and determine whether or not the coefficient of the variable "level of education" (i.e., X2) is significantly different from zero. Let α = 0.05. c. At α = 0.05, perform an F-test and determine whether or not the regression model is significant. d. As you note, the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient.
Shaiju T.
Use the data in PHILLIPS to answer these questions. $\begin{array}{l}{\text { (i) Using the entire data set, estimate the static Phillips curve equation } i n f_{t}=\beta_{0}+\beta_{1} \text { unem_{t} }+u_{t}} \\ {\text { by OLS and report the results in the usual form. }}\end{array}$ $\begin{array}{l}{\text { (ii) Obtain the OLS residuals from part (i), } \hat{u}_{t} \text { and obtain } \rho \text { from the regression } \hat{u}_{t} \text { on } \hat{u}_{t-1} . \text { (It is fine }} \\ {\text { to include an intercept in this regression.) Is there strong evidence of serial correlation? }}\end{array}$ $\begin{array}{l}{\text { (iii) Now estimate the static Phillips curve model by iterative Prais-Winsten. Compare the estimate }} \\ {\text { of } \beta_{1} \text { with that obtained in Table } 12.2 . \text { Is there much difference in the estimate when the later }} \\ {\text { years are added? }}\end{array}$ $\begin{array}{l}{\text { (iv) } \quad \text { Rather than using Prais-Winsten, use iterative Cochrane-Orcutt. How similar are the final }} \\ {\text { estimates of } \rho ? \text { How similar are the PW and CO estimates of } \beta_{1} \text { ? }}\end{array}$
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