Question 3 Consider a multiple regression model predicting Calories = 6.53+ 30.84 BMIl + 90.14 Gender + 30.94 Age, where BMI is body mass index ( ), gender (0 for males and 1 for females). height Assume all variables are statistically significant at a 5% level. When interpreting the model, is true to say that, females intake, on average, 90.14 more calories than males, holding everything else constant.
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- You have data on the training regime of 100m elite runners. For each runner you observe their best run of the year (in second) (pb), the number of hours they train each week (tr) and a dummy variable equal to 1 if thei are male (male). Using OLS you get the following regression: pb= 36.2 1.3male -0.92tr +0.009tr² -0.09male tr +0.001male * (tr²) How many hours should a male elite runner train each week to minimize the time of their best run of the year? (round to the closest decimal)In exercise 1, the following estimated regression equation based on 10 observations was presented. y^=29.1270+.5906x1+.4980x2Here SST=6724.125, SSR=6216.375, sb1=.0813, and sb2=.0567. a) Compute MSR and MSE. b) Compute F and perform the appropriate F test. Use α=.05. c) Perform a t test for the significance of β1. Use α=.05. d) Perform a t test for the significance of β2. Use α=.05.This exercise refers to the drunk driving panel data regression, summarizedin Regression analysis of Drunk Driving (see attachment)a. New Jersey has a population of 8.85 million people. Suppose that NewJersey increased the tax on a case of beer by $2 (in 1988 dollars). Use theresults in column (5) to predict the number of lives that would be savedover the next year. Construct a 99% confidence interval for your answer. b. The drinking age in New Jersey is 21. Suppose that New Jersey loweredits drinking age to 19. Use the results in column (5) to predict the changein the number of traffic fatalities in the next year. Construct a 95% confidence interval for your answer.c. Suppose that real income per capita in New Jersey increases by 3% inthe next year. Use the results in column (6) to predict the change in thenumber of traffic fatalities in the next year. Construct a 95% confidenceinterval for your answer.d. How should standard errors be clustered in the regressions in columns(2) through…
- A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the modet: Sales- Bo + B1 Advertising +t. The following table shows a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 40.10 14.08 2.848 0.0052 Advertising 2.88 1.52 -1.895 0.0608 Which of the following are the competing hypotheses used to test whether the slope coefficient differs from 3? Multiple Choice Ho i bị 3; HAtbi3 Họ ib - 2.88; HAibi 2.88Suppose that a researcher, using wage per hour data on 250 randomly selected male workers and 280 female workers, estimates the following OLS regression wage - 12.68+2.79xMale (0.18) (0.84) R = 0.06, s-3.10 where Male is a dummy variable that takes the value 1 if the worker is male and 0 if female: s represents the standard error of the regression and in brackets homoskedastic std errors are reported. The researcher wants to find the gender pay gap as percentage bf the wagé per hour of women. According to this information the gender pay gap on average against women is approximately -22% -25% -38% O-16%Consider a linear causal model Ya+BX+yW+u, with cov(X, W) > 0. Suppose we do not observe the variable W and have to omit it from the regression, then O OLS is expected to be larger than 3 in large samples. BOLS is expected to be equal to 3 in large samples. OLS is expected to be smaller than 3 in large samples. Since we do not know whether X and u are correlated and the sign of y, there is not enough information to compare OLS and B.
- Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm³, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. Regression Analysis: cuberoot (Volume) versus Time Predictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Time 0.640 0.000018 35512.6 0.000 s=0.030 R-Sq=1.000 R-sq (adj)=1.000 What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Volume = 0.640 - 0.006(Time) Volume = -0.006 + 0.640(Time) Volume = - 0.006 + 0.640(Time?)Test Design: Suppose I want to test the impact of soccer coaches on soccer teams. How would you test this? Include a few (3 or 4) independent variables to explain the dependent variable. Describe the data and write the regression equation.A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 A) Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
- Discuss the FIVE (5) importance of adding error term in the regression model.You 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 +…A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: Sales 6g + 61 Advertising + e. The following table shows a portion of the regression results. Coefficients Standard Error t-stat p-value 40.10 14.88 2.848 0.0052 Intercept Advertising 2.88 1.52 -1.895 0.0608 When testing whether Advertising is significant at the 10% significance level, the conclusion is to Multiple Choice reject Hg, we can conclude advertising is significant not reject He; we cannot conclude advertising is significant reject He; we cannot conclude advertising is significant not reject He; we can conclude advertising is significant