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Explain Distribution of Regression Statistics with Normal Errors?
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- In a regression model, if the variance of the dependent variable, y, conditional on an explanatory variable, x, or Var(y/x), is not constant, a. the t statistics are invalid and the confidence intervals are valid for small sample sizes. b. the t statistics are valid and the confidence intervals are invalid for small sample sizes. c. the t statistics and the confidence intervals are valid no matter how large the sample size. d. the t statistics and the confidence intervals are both invalid no matter how large the sample size. O a. a O b. b О с. C ○ d. dYou are interested in how the number of hours a high school student has to work in an outside job has on their GPA. In your regression you want to control for high school standing and so you run the following regression: GPA = 3.4 0.03 * HrsWrk - 0.7 * Frosh - 0.3 * Soph +0.1 * Junior (1.1) (0.013) (0.23) (0.14) (0.08) where HrsWrk is the number of hours the student works per week, and Frosh, Soph, and Junior are dummy variables for the student's class standing. a) If you include a dummy variable for seniors, that would cause a Hint: type one word in each blank. For the rest of questions, type a number in one decimal place. b) The expected GPA of a Sophomore who works 10 hours per week is c) The expected GPA of a Senior who works 10 hours per week is d) If Dom and Sarah work the same number of hours per week, but Dom is a Junior and Sarah is a Freshman. Dom is expected to have a higher GPA than Sarah. e) Suppose you rewrite the regression as: problem. GPA = ₁HrsWrk + ß2Frosh + B2Soph +…Suppose you run the following regression: outcome=alpha0 + alpha1*female + alpha2*married + epsilon. You know that female equals 1 for females and 0 otherwise. You know that married equals 1 if the person is married and 0 otherwise. What is the estimated outcome for non-married respondents who are not female?
- An analyst working for your firm provided an estimated log-linear demand function based on the natural logarithm of the quantity sold, price, and the average income of consumers. Results are summarized in the following table: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept LN Price LN Income df 0.968 0.937 0.933 0.003 30 SS MS F 2 0.003637484 0.001818742 202.48598 0.000242516 8.98206E-06 27 29 0.00388 Coefficients Standard Error 0.57 0.00 0.13 0.51 -0.08 0.15 t Stat 0.90 -19.50 1.13 P-value 0.37 0.00 0.27 Significance F 5.55598E-17 Lower 95% -0.65 -0.09 -0.12 How would a 4 percent increase in income impact the demand for your product? Demand would increase by 60 percent. Demand would increase by 0.6 percent. Demand would decrease by 60 percent. Demand would decrease by 0.6 percent. Upper 95% 1.68 -0.07 0.41The data for this question is given in the file 1.Q1.xlsx(see image) and it refers to data for some cities X1 = total overall reported crime rate per 1 million residents X3 = annual police funding in $/resident X7 = % of people 25 years+ with at least 4 years of college (a) Estimate a regression with X1 as the dependent variable and X3 and X7 as the independent variables. (b) Will additional education help to reduce total overall crime (lead to a statistically significant reduction in crime)? Please explain. (c) Will an increase in funding for the police departments help reduce total overall crime (lead to a statistically significant reduction in total overall crime)? Please explain. (d) If you were asked to recommend a policy to reduce crime, then, based only on the above regression results, would you choose to invest in education (local schools) or in additional funding for the police? Please explain.18 Calculate the least square regression líne equation with the given X and Y values. Consider the values: X Y 60 3.1 61 3.6 62 3.8 63 4 65 4.1 To Find, Least Square Regression Line EquationY = a+ b X
