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- In a typical multiple linear regression model where x1 and x2 are non-random regressors, the expected value of the response variable y given x1 and x2 is denoted by E(y | 2,, X2). Build a multiple linear regression model for E (y | *,, *2) such that the value of E(y | x1, X2) may change as the value of x2 changes but the change in the value of E(y | X1, X2) may differ in the value of x1 . How can such a potential difference be tested and estimated statistically?Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211 (a) Develop an estimated regression equation relating y to x1. (Round your numerical values to one decimal place.) ŷ = Predict y if x1 = 51. (Round your answer to one decimal place.) (b) Develop an estimated regression equation relating y to x2. (Round your numerical values to one decimal place.) ŷ = Predict y if x2 = 19. (Round your answer to one decimal place.) (c) Develop an estimated regression equation relating y to x1 and x2. (Round your numerical values to one decimal place.) ŷ = Predict y if x1 = 51 and x2 = 19. (Round your answer to one decimal place.)Contains 20 observations on the response variable y along with the predictor variables x and d. y x d 26 80 1 16 80 1 24 59 0 13 51 0 17 55 0 16 55 1 8 20 0 15 35 1 21 48 0 17 42 0 20 78 1 14 52 1 20 62 0 15 32 0 23 45 1 6 27 0 17 65 0 22 59 1 8 21 0 15 30 1 a. Estimate a regression model with the predictor variables x and d, and then extend it to also include the interaction variable xd. What is the estimated regression coefficient for the predictor variable x in both models? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) ) Model 1(No Interaction) = Model 2 (Interaction)= a-2. Use the preferred model to predict y. (Round coefficient estimates to at least 4 decimal places and final answers to 2 decimal places.) Predictor Variables Predicted Y x=15, d=0 ? x=15, d=1. ?
- 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.Which of the following is NOT a good reason for including a disturbance term in a regression equation? Select one: a. It captures omitted determinants of the dependent variable b. To allow for errors in the measurement of the dependent variable c. To allow for random influences on the dependent variable d. To allow for the non-zero mean of the dependent variableThe Head of production at Amiba private limited needed to examine the key determinants of company profitability($,000). So, he collected relevant(monthly) data and following is the summary of his regression output. SUMMARY OUTPUT Regression Statistics Multiple R 0.5776 R Square 0.3336 Adjusted R Square 0.2670 Standard Error 2.2743 Observations 34 ANOVA df SS MS F Significance F Regression 3 77.6774 25.8925 5.0060 0.0062 Residual 30 155.1693 5.1723 Total 33 232.8467 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 10.49 2.9211 3.5927 0.0012 4.5291 16.4605 4.5291 16.4605 Variable X 0.99 1.2461 0.7937 0.4336 -1.5559 3.5340 -1.5559 3.5340 Variable Y 2.56 1.1291 2.2663 0.0308 0.2529 4.8648 0.2529 4.8648 Variable Z 2.06…
- The Head of production at Amiba private limited needed to examine the key determinants of company profitability($,000). So, he collected relevant(monthly) data and following is the summary of his regression output. SUMMARY OUTPUT Regression Statistics Multiple R 0.5776 R Square 0.3336 Adjusted R Square 0.2670 Standard Error 2.2743 Observations 34 ANOVA df SS MS F Significance F Regression 3 77.6774 25.8925 5.0060 0.0062 Residual 30 155.1693 5.1723 Total 33 232.8467 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 10.49 2.9211 3.5927 0.0012 4.5291 16.4605 4.5291 16.4605 Variable X 0.99 1.2461 0.7937 0.4336 -1.5559 3.5340 -1.5559 3.5340 Variable Y 2.56 1.1291 2.2663 0.0308 0.2529 4.8648 0.2529 4.8648 Variable Z 2.06…The accompanying data file contains 40 observations on the response variable y along with the predictor variables x and d. Consider two linear regression models where Model 1 uses the variables x and d and Model 2 extends the model by including the interaction variable xd. Use the holdout method to compare the predictability of the models using the first 30 observations for training and the remaining 10 observations for validation. y x d 70 11 1 102 19 1 76 12 1 83 14 1 61 17 0 62 13 0 67 20 0 98 16 1 84 11 1 101 15 1 51 16 0 108 16 1 32 13 0 71 15 1 101 17 1 90 15 1 112 19 1 88 13 1 110 18 1 95 17 1 44 14 0 51 19 0 112 17 1 113 17 1 52 13 0 61 10 1 100 16 1 78 14 1 90 16 1 57 16 0 59 15 0 53 15 0 119 19 1 109 18 1 68 11 0 104 19 1 45 18 0 67 17 0 65 15 0 74 14 1 1. Use the training set to estimate Models 1 and 2. Note: Negative values should be indicated by a minus sign. Round your answers to 2…The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = (b) Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
- a) Interpret the significant level of hypothesis for three independent variables in this model. b) Calculate the value of dependent value, y given that X1 = 3.5, X2 = 2.9 and X3 = 4.1.A statistical program is recommended. Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211 (a) Develop an estimated regression equation relating y to x1. (Round your numerical values to one decimal place.) ŷ = 45.1+1.9x1 Predict y if x1 = 59. (Round your answer to one decimal place.) ____ (b) Develop an estimated regression equation relating y to ,x2.(Round your numerical values to one decimal place.) ____ ŷ = mPredict y if x2 = 13. (Round your answer to one decimal place.)____ C) Develop an estimated regression equation relating y to x1 and x2.(Round your numerical values to one decimal place.) ŷ = ____ Predict y if x1 = 59 and x2 = 13. (Round your answer to one decimal place.)___In a data set with 12 observations, you try fitting two regression models. The esti-mated models are summarized as: Model 1: Y(hat) =3.5 + 2x; SSR= 5, and SSE= 10;Model 2: Y(hat) =3.0 + 1.5x + 0.4^2; SSR=23, and SSE=7 (a) Calculate R2 for both models. b. for both models test the null hypothesis that all the regression coefficients other than the intercept are 0.