Let be the residual for observation i for an estimated regression model. If 1.2 and ez = -0.33 R2 is definitely less than 1 O R2 is definitely greater than 1 O R2 is definitely greater than 0 O RSS is definitely positive O Both (a) and (d) are correct answers.
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- Suppose we estimated our multiple linear regression, all of the variables have p values below 0.05 (so they are statistically different from zero) but the intercept has p-value equal to p=0.343. What does it mean?Which of the assumptions below is NOT an assumption relating to the classical regression model: A. Var (₁)=σ² <∞ B. var (y, )=k<∞ C. cov (&,&-) = 0 for s=0 OD. E(E)=0The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGE: = Bo + B₁ EDUC; + &i where WAGE; is the hourly wage of person i (i.e., any specific person) and EDUC; is the number of years of education for that same person. The residual ₂ encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGE;= -10.7+ 3.1 EDUC; If the standard error of the estimate of B₁ is 1.04, then the true value of B₁ lies between grows, you would expect this range to in size. and . As the number of observations in a data set
- Why has the quantity of reserves needed to maintain an "abundant" reserve system increased from $35 billion in 2008 to $2.3 trillion in 2022? What are the implications of this change?I estimate a multiple linear regression model with three explanatory variables and a sample size of 363 observations. The RSS of this model is 0.428217, the adjusted R squared is 0.453103. When I regress the depended variable on a constant only, I find that the RSS of this simple model is 0.789537 The value of the realized F stat for the test on the significance of the regression is: Select one: Ⓒa. 100.9721 and the null is that all betas except the intercept are simultaneously equal to zero O b. 145.056123 and the null is that the model is in the overall significant for the population statistically at 1% significance level 145.056123 and the null is that all betas are simultaneously equal to zero Gm. My Moodle O c. O d. 145.056123 and the null is that all betas except the interecpt are simultaneously equal to zero O e. 100.9721 and the null is that all betas are simultaneously equal to zero Clear my choiceThe 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.
- Please no written by hand solution a) Suppose in a regression of weekly salaries on years of schooling for males(m) and females(f), the following results are obtained. Wm = 50Sm and Wf = 40Sf. where Wm (Wf) denotes weekly salary and Sm (Sf) denotes years of schooling for males and females respectively. 50 and 40 are the coefficients on schooling in the male and female regression respectively. On average, men have 12 years of schooling and women have 10 years of schooling. What is the average male-female wage differential? Is this a good estimate of discrimination? Explain why/why not. Using the information in the question, what would you propose as a better estimate of discrimination? State any assumptions that you use and explain your answer.The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute Time (minutes), x Well-Being Index Score, y 5 72 105 20 25 35 60 69.2 68.0 67.5 67.1 65.9 66.0 63.8 (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. ŷ=x+ (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For every unit increase in commute time, the index score falls by (Round to three decimal places as needed.) OB. For every unit increase in index score, the commute time falls by (Round to three decimal places as needed.) 1 D. For an index score of zero, the commute time is predicted to be (Round to three decimal places as needed.) on average. on average. OC. For a commute time…An example of a cubic regression model is Yi= 30 + B1X + 32x2 + 33x³ + ui Yi = 30 + B1X + 32x² + ui. Yi = 30 + ß1ln(X) + ui Yi= 30 + 31X + B2Y2 + ui.
- Consider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted value of Y in each case? a. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 b. x1 = 23, x2 = 18, x3 = 10, and x4 = 11 c. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 d. x1 = -10, x2 = 13, x3 = -8, and x4 = -16Hello, please help me to solve the question (c) and (d) below.Consider this regression model (1) : Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4 Xt + εt ; where t= 1, ..., 75.We use OLS to estimate the parameters, producing the following model:Ŷt = 1.115 + 0.790 Ut − 0.327 Vt + 0.763 Wt + 0.456 Xt (0.405) (0.178) (0.088) (0.274) (0.017) Given that:R2 = 0.941; Durbin Watson stat DW = 1.907; RSS = 0.0757.(To answer the question, use the 5% level of significance, state clearly H0 and H1 that are tested, the test statistics that are used, and interpret the decisions.) (a) Describe the concepts of unbiasedness and efficiency. State the conditions required of regression (1) in order that the OLS estimators of the model parameters possess these properties. (b) Perform the following tests on the parameters of regression (1): (i) test whether the parameters β1, β2, β3 and β4 are individually statistically significant; (ii) test the overall significance of the regression model;…
