Suppose that a researcher, using wage data on 200 randomly selected male workers and 240 female workers, estimates the OLS regression W age ˆ = 10 (0.2) + 2 (0.4) × M ale, R2 = 0.10, SER = 4, where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 if the person is a male and 0 if the person is a female. Define the wage gender gap as the difference in mean earnings between men and women. 1. What is the estimated gender gap? 2. Is the estimated gender gap significantly different from 0? (Compute the p-value for testing the null hypothesis that there is no gender gap.) 1 3. Construct a 95% confidence interval for the gender gap. 4. In the sample, what is the mean wage of women? Of men? 5. Another researcher uses these same data but regresses Wages on Female, a variable that is equal to 1 if the person is female and 0 if the person a male. What are the regression estimates calculated from this regression? W age ˆ = _ + _ × F emale, R2 = _, SER = _.

Suppose that a researcher, using wage data on 270 randomly selected male workers and 302 female workers, estimates the OLS regression Wage = 13.522 + 2.290 × Male, R = 0.05, SER=4.5, (0.2484) (0.3888) where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 if the person is a male and 0 if the person is a female. Define the wage gender gap as the difference in mean earnings between men and women. What is the estimated gender gap? The estimated gender gap equals $2.29 per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho: B = 0 versus H4:B1 #0. The t-statistic for testing the null hypothesis that there is no gender gap is 5.89 . (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap is (Round your response to four decimal places.)

Suppose that a researcher, using data on class size (CS) and average test scores from 102 third-grade classes, estimates the OLS regression TestScore=515.196+ (-5.7618)x CS, R² = 0.06, SER=11.4. A classroom has 23 students. The regression's prediction for that classroom's average test score is (Round your response to two decimal places.) Last year a classroom had 20 students, and this year it has 24 students. The regression's prediction for the change in the classroom average test score is (Round your response to two decimal places.) The sample average class size across the 102 classrooms is 21.19. The sample average of the test scores across the 102 classrooms is (Hint: Review the formulas for the OLS estimators.) (Round your response to two decimal places.)

A researcher believes that there is a linear association between the level of potassiumcontent (y) in milligrams and the amount of fiber (x) in grams in cereal. The regression line forthe data is computed to be: ŷ = 36+27x rate. It was also computed that r = .62 b. If a cereal has 4 grams of fiber and a potassium content of 160 milligrams, what is thevalue of the residual?

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Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. What is the subpopulation mean when x = 7 servings per day?

A) Compute the last-squares regression line for predicting US emission from NON US - emissions. b) If the non-US emission differ by 0.2 from one year to the next by how much would you predict the US- emission to differ?

Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is: kids; = Bo + B1educ; + uż. 1. What are the parameters in the model? 2. What kinds of factors are contained in u? Are these likely to be cor- related with level of education? 3. Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.

A study reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment. With age = x and ACBG = y, summary values are n = 26, Ex; = 1620, 2(x₁ - x)² = 3756.96, y₁ = 281.9, (y₁ - y)² = 465.34, and Ex,y; = 16,733. (a) Compute a 90% CI for the true correlation coefficient p. (Round your answers to four decimal places.) (b) Test Ho: p = -0.5 versus H₂: P < -0.5 at level 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = State the conclusion in the problem context. O Reject Ho. There is no evidence that p < -0.5. O Fail to reject Ho. There is evidence that p < -0.5. O Reject Ho. There is evidence that p < -0.5. O Fail to reject Ho. There is no evidence that p < -0.5. (c) In a regression analysis of y on x, what proportion of variation in change of cortisol-binding globulin level could be explained by…

A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…