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Discuss the FIVE (5) importance of adding error term in the regression model.
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- Distinguish between the R2 and the standard error of a regression. How doeach of these measures describe the fit of a regression?What is difference between regression model, and estimated regression equation?Consider the regression model Yi = b0 + b1X1i + b2X2i + ui. Use approach 2from Section 7.3 to transform the regression so that you can use a t-statistic to testa. b1 = b2.b. b1 + 2b2 = 0.c. b1 + b2 = 1. (Hint: You must redefine the dependent variable in theregression.)
- In multiple OLS regressions, if you are using power terms to fit for nonlinearity, how do you interpret the coefficients? For example: Yi=B1+B2X+B3X^2+Ui and B2 and B3 are both significant.Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied whena) Zi is independent of (Yi, Xi, Wi)?b) Zi=Wi?c) Wi is1 for all i?d) Zi=Xi?What is the functional form of this equation? What are the advantages and limitations of this functional form? Interpret precisely the coefficients of Px and Py in the regression.
- All the regression assumptions lie on the residuals, for both simple and multiple regression. True or False?In multiple regression model: what is it means for a variable to be significant? Explain the meaning of the significant variable.Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…
- From the following data, determine if the data has a positive or a negative relationship with each other. Showcase the regression line, and determine if the data provided fits the approximate curve.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)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?