Suppose you have the regression model below with 50 observations. Z: = 2.80 +3.76Time- O.25Z1 Considering significance level of 5%, what will be the critical table value for stationarity test? Select one: O a.-3.00 O b.-4.15 O C-4.38 O d.-3.60 O e. -2.93 O f1358
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- Use the following STATA output to test whether the variable wgt is significant at 5% level: Source | SS df Number of obs = EC 3. Prob > F R-squared MS 392 300.76 0.0000 0.6993 Adj R-squared anba6970 4.2965 388) = Model Juu16656.4443 Residual 162,54916 5552.1481 388 18.4601782 Total Juu23818.9935 391 60.9181419 Root MSE Coef. Std. Err. P>It| [95% Conf. Interval] syl ena wat .2677968 -.012674 -.0057079 44.37096 .4130673 .0082501 .0007139 1.480685 -0.65 -1.54 -8.00 29.97 0.517 0.125 0.000 0.000 -1.079927 -.0288944 -.0071115 41.45979 .5443336 0035465 .0043043 47.28213 _cons The variable is not significant because p-value is less than 0.05. The variable is significant because p-value is less than 0.05. The variable is significant because p-value is less than 0.1. The variable is not significant because p-value is greater than 0.05OA linear regression model is Units 3,414-0.839xWeek. For week 45, what is the forecast for the number of units? Round your answer to the nearest whole number. OO units1. R-squaredSuppose regression of y on an intercept and x with 50 observations yields total sum of squares 100 andexplained sum of squares 36.(a) What is ?^2?(b) What is the correlation coefficient between y and x?(c) What is the standard error of the residual?
- 5. The following estimated equation was obtained by OLS regression using quarterly data for 1978 to 1996 inclusive. Yt = 2.20+ 0.104Xt₁ - 3.48 Xt₂ + 0.34Xt3 (3.4) (0.005) (2.2) (0.15) Standard errors are in parentheses, the explained sum of squares was 109.6, and the residual sum of squares 18.48. a. Test at the 5% level for the statistical significance of the parameter estimates. b. Calculate the coefficient of determination.4. The estimation of the model with quarterly car sales in the U.S. from 1975 to 1990 gives: Source | df MS Number of obs = 64 F( 2, Prob > F 61) = 12.21 Model .32720224 2 .16360112 0.0000 Residual | .817286587 61 .013398141 R-squared Adj R-squared = 0.2625 Root MSE 0.2859 Total | 1.14448883 63 .018166489 .11575 lqne | cCoef. t P>|t| std. Err. [95% Conf. Interval] 1price lincome -.4604611 3.37186 6.89398 -.8280926 .1838504 -4.50 0.000 -1.195724 2.399991 . 4860261 4.94 0.000 1.428121 _cons 5.92543 .4843662 12.23 0.000 4.95688 Based on the parameter estimates, what is the predicted effect of a 10% increase in price on the number of cars sold? What would be the effect of that price increase on the value of car sales?b. A regression on the original regressors, q₁² and a constant term yields the following statistics: R2 0.296041 F = 1.177507 coeff of q² has a t-statistic of 2.876 (i) With this information, which test can you implement to deal with the problem omitted variables and why? (ii) Implement the test as stated in b(i) and interpret the results. (iii) What is (are) the consequence(s) of the problem alluded to above on the estimators?
- A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output. Predictor Coef SE Coef t-ratio Constant -124.13 78.712 0.046 Math 1.223 0.1966 6.220 0.000 S = 34.55 R-Sq = 82.8% R-Sq (Adj) = 83.5% Which of the following represents the standard deviation of the residuals? O 1.223 34.55 78.712 124.13You estimated a regression with the following output. Source | SS df MS Number of obs = 289 -------------+---------------------------------- F(1, 287) = 41986.64 Model | 664544048 1 664544048 Prob > F = 0.0000 Residual | 4542496.25 287 15827.5131 R-squared = 0.9932 -------------+---------------------------------- Adj R-squared = 0.9932 Total | 669086544 288 2323217.17 Root MSE = 125.81 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 43.81013 .2138056 204.91 0.000 43.38931 44.23096 _cons | 49.31707 16.96222 2.91 0.004 15.93094 82.70319…1. Suppose have the sample linear regression function: we Y = B, + B,X, +e,, Bo and B are OLS estimates, prove the following equations hold: Ee, = 0 а. %3D b. Se,x, = 0, x, is the deviation form of Xi EeÝ, = 0 c. d. Y = Y 2. Suppose the sample size n=10, we have the following figures for the sample data: ΣΥ-1110; ΣΧ-1 680; ΣΧY -204200 | ΣΧ31 5400; ΣΥ-133300 The representation of PRF is Y = b, +b,X, +u,, u, O iid N(0,4) The OLS estimates for the SRF is ß, and B a. calculate B, and B with the above figures. b. calculate the standard error of B, and B- c. calculate the determination coefficient: R? d. construct 95% confidence interval for b, and b, respectively. e. conduct hypothesis test: HO: b, =0, H1: b, #0. f. conduct hypothesis test: HO: b, =1, H1: b, #1.
- 12- Which of the following is true in case of measurement error in the regressor? a) O Predictors are biased and consistent 35 b) O Predictors are unbiased and consistent C) O Predictors are unbiased and inconsistent d) O Predictors are biased and inconsistent Leave blank(a) Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. X-values (a) Choose the best answer for residuals plot (a). O A. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. O B. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. O C. The scattered residuals plot indicates an appropriate linear model. (b) Choose the best answer for residuals plot (b). O A. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. O B. The scattered residuals plot indicates an appropriate linear model. O C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power increases as the values of the explanatory variable increases. (c) Choose…Exercises 5.1 Suppose that a rescarcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression TestScore- 520.4 - 5.82 x CS, R² =0.08, SER = 11.5. (20.4) (2.21) a. Construct a 95% confidence interval for B, the regression slope coef- ficient. b. Calculate the p-value for the two-sided test of the null hypothesis Hs B1 -0. Do you reject the null hypothesis at the 5% level? At the 1% level?