a) Compute the linear regression line y=bo+b₁x b) What is the estimated value, y for x = 7?
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- A “Cobb–Douglas” production function relates production (Q) to factorsof production, capital (K), labor (L), and raw materials (M), and an errorterm u using the equation Q = λKβ1Lβ2Mβ3eu, where λ, β1, β2, and β3 areproduction parameters. Suppose that you have data on production and thefactors of production from a random sample of firms with the same Cobb–Douglas production function. How would you use regression analysis toestimate the production parameters?1. Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.23. Compute the actual values indicated by A,B,C and D in that order. A. 2569, 560, 996553, 87103 B. 996553, 2569, 87103, 560 C. 650, 632699, 18730, 9562 D. 2695, 650, 633599, 17830 24. If the general linear regression model is given by the equation: y=a+bx; considering the information obtained in figure 2, compute the value of b. A. 210.185 B. 121.852 C. 21.850 D. 2.185 25. If the general linear regression model is given by the equation: y=a+bx; considering the information obtained in figure 2, compute the value of a. A. 397.210 B. 973.102 C. 210. 379 D. 237.021
- Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n observations on x and y, you estimate the model by OLS and obtain the estimates βˆ 0, βˆ 1, and the R-squared of the regression, R2 . Then you scale this sample by a factor of 100, obtain a new sample {xi/100; yi/100} for i = 1, . . . , n, re-estimate the model by OLS, and denote the new coefficient estimates by β˜ 0, β˜ 1, and the new R-squared of the regression by R˜2 . a) Give the expression of β˜ 1 in terms of βˆ 1, and justify your answer.Consider the following regression model Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4Xt + ∈t , where U, V, W, X and Y are economic variables observed from t = 1, . . . , 75, β0 , . . . , β4 are the model parameters and ∈t is the random disturbance term satisfying the classical assumptions. Ordinary Least Squares (OLS) is used to estimate the parameters, producing the following estimated model: Yt = 1.115 + 0.790*Ut − 0.327*Vt + 0.763*Wt + 0.456*Xt (0.405) (0.178) (0.088) (0.274) (0.017) where standard errors are given in parentheses, the R-squared = 0.941, the Durbin-Watson statistic is DW = 1.907 and the residual sum of squares is RSS = 0.0757. In answering this question, use the 5% level of significance for any hypothesis tests that you are asked to perform, state clearly the null and al- ternative hypotheses that you are testing, the test statistics that you are using and interpret the decisions that you make.…The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents. xx 11.5 8.5 6.7 3.5 2.9 2.7 2.7 0.9 yy 14.1 11 10 7.3 6.7 6.4 6.4 4.7 Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. Round to 2 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 10.2 thousand automatic weapons? Round to 3 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 5.8 thousand automatic weapons? Round to 3 decimal places.
- The following table gives the marks obtained by 10 students in POLI 344 (X) together with the marks obtained in the exam in POLI 308 (Y). POLI 344 (X)8 8 9 10 10 11 12 13 13 11 14 POLI 443 (Y) 7 11 8 7 12 11 10 12 14 17 15 (i) State the two equation lines of the regression line. (ii) If a student was absent from POLI 443 but scored 18 in POLI 344 (X) state the regression line, which would be suitable for estimating his/her possible mark in POLI 443 and work out a fair estimate for his /her possible mark.31 - Find the regression model. Regresyon modelini bulunuz. Y X 2 5 5 9 7 4 4 11A) y=-3,21+2,11xB) y=2,56+5,43xC) y=5,27+0,11xSuppose a researcher, using wage data on 200 randomly selected maleworkers and 240 female workers, estimates the OLS regression ''Wage'' = 10.73 + 1.78 X Male, R2 = 0.09, SER = 3.8, (0.16) (0.29)where Wage is measured in dollars per hour and Male is a binary variablethat is equal to 1 if the person is a male and 0 if the person is a female.Define the wage-gender gap as the difference in mean earnings betweenmen and women.a. What is the estimated gender gap?b. Is the estimated gender gap significantly different from 0? (Computethe p-value for testing the null hypothesis that there is no gender gap.)c. Construct a 95% confidence interval for the gender gap.d. In the sample, what is the mean wage of women? What is the meanwage of men?e. Another researcher uses these same data but regresses Wages on Female, a variable that is equal to 1 if the person is female and 0 if the person is male. What are the regression estimates calculated from this regression?"Wage" =______ +________ X Female,…
- For these (x,y) pairs of data points: 1,5 3,7 4,6 5,8 7,9 Compute . Compute . What is the equation of the regression line?Use the following results obtained from a simple linear regression analysis with 12 observations. Y = 37.2895- (1.2024)X Sb = 0.2934 Test to determine if there is a significant negative relationship between the independent and dependent variables at alpha= .05. Give the resulting conclusion. a. is rejected. B.cannot be tested with the given information. c. is not rejected. D. is not an appropriate null hypothesis for this situation.A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 52.3 45.6 49.1 55.9 48.7 53.1 46.5 47.4 45.9 52 45.6 59.8 48.9 45.5 52.6 46.2 35.1 71.2 28.8 32.6 33.5 40.7 41 40.3 43.7 40 65.8 47 37.8 52.8 34.2 28 53.5 R2=R2= (Not the adjusted R2R2) FF test statistic = P-value for overall model = test statistic for b1b1 p-value for the two-tailed test = test statistic for b2b2 p-value for the two-tailed test = What is your conclusion for the overall regression model at the 0.05 alpha level (also called the omnibus test)? The overall regression model is statistically significant at α=0.05α=0.05. The overall…