Consider the following regression model and corresponding output for a dataset with n = 104 observations: y=ß₁+b2x2+3x+4x+u Variable β Std. Error t P>|t| X2 X3 X4 -0.012 0.006 -2.289 0.022 0.596 0.014 41.139 0.000 0.52 1.06 Constant 8.860 1.766 What is the marginal effect of x4 on y? (approximate at least to 3 decimal places) 5.017 0.000
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- Consider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.Consider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2 (effect of change in X1, holding X2 constant).b. ΔY/ΔX2 = β2 + β3X1 (effect of change in X2, holding X1 constant).c. If X1 changes by ΔX1 and X2 changes by ΔX2, then ΔY =(β1+β3X2)ΔX1 + (β2 + β3X1)ΔX2 + β3ΔX1ΔX2.Consider the simple regression model: y=0.56+1.56x+u Using this and assuming the estimated Var(y)=0.64 and the estimated Var(x)=3.07, what is the estimated Var(x+y)?
- A simple regression analysis to estimate the demand for Chick-fil-A’s new premium super-sized spicy chicken sandwich is Q= 48-2p. If Chick-fil-A sets the price at $12 and Q=20, calculate the regression’s error term? Also, list five assumptions of the classical linear regression model.Suppose you have the following data: X Y 3 9 7 45 5 25 2 8 Using OLS methods: estimate the following regression model: Sq root of Yi = Beta0 + Beta1(Xi) + errorConsider the regression model Yi = β0 + β1Xi + ui.a. Suppose you know that β0 = 0. Derive a formula for the least squaresestimator of β1.b. Suppose you know that β0 = 4. Derive a formula for the least squaresestimator of β1?
- True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.Given the following regression output, Predictor Coefficient SE Coefficient t p-value Constant 84.998 1.863 45.62 0.000 x1 2.391 1.200 1.99 0.051 x2 -0.409 0.172 -2.38 0.021 Analysis of Variance Source DF SS MS F p-value Regression 2 77.907 38.954 4.138 0.021 Residual Error 62 583.693 9.414 Total 64 661.600 answer the following questions: d-1. State the decision rule for 0.05 significance level: H0: β1 = β2 = 0; H1: Not all β's are 0. (Round your answer to 2 decimal places.) d-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) d-3. What is the conclusion? Use the 0.05 significance level.Consider the following multiple regression Price=118.9+0.594BDR+23.5Bath+0.195Hsize+0.004Lsize+0.095Age−48.5Poor, R2=0.75, SER=41.5 (22.7) (2.56) (8.56) (0.017) (0.00049) (0.315) (10.7) The numbers in parentheses below each estimated coefficient are the estimated standard errors. A detailed description of the variables used in the data set is available here . Suppose you wanted to test the hypothesis that BDR equals zero. That is, H0: BDR=0 vs H1: BDR≠0 Report the t-statistic for this test. The t-statistic is ________ (Round your response to three decimal places)
- Consider a regression in which a coefficient suffers from downward omitted variable bias. If you add a regressor that controls for the omitted variable bias: Group of answer choices 1. Can’t determine 2. The new estimate will be smaller. 3. The new estimate will remain unchanged. 4. The new estimate will be largerPast class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.Given the following regression output, Predictor Coefficient SE Coefficient t p-value Constant 84.998 1.863 45.62 0.000 x1 2.391 1.200 1.99 0.051 x2 -0.409 0.172 -2.38 0.021 Analysis of Variance Source DF SS MS F p-value Regression 2 77.907 38.954 4.138 0.021 Residual Error 62 583.693 9.414 Total 64 661.600 answer the following questions: Write the regression equation. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) If x1 is 4 and x2 is 11, what is the expected or predicted value of the dependent variable? (Round your answer to 3 decimal places.) How large is the sample? How many independent variables are there?