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16 | The margin of error for a 95% confidence interval for β₁ is, | |||||
a | 1.0045 | |||||
b | 1.0574 | |||||
c | 1.1130 | |||||
d | 1.1716 |
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- 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 significantA 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 2.88Numerical Answer Only Type Question Enter the numerical value only for the correct answer in the blank box. If a decimal point appears, round it to two decimal places. Assume that the number of visits by a particular customer to a mall located in downtown Toronto is related to the distance from the customer's home. The following regression analysis shows the relationship between the number of times a customer visits(Y)per month and the distance(X, measured in km) from the customer's home to the mall. \[ Y=15-0.5 X \] A customer who lives30 kmaway from the mall will visi______ who lives10 km away. less times than a customer
- 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 +…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.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)
- This regression is based on cross-section data of 1744 individuals and the relationship between their weekly earnings (in dollars) and age (in years) during 2020. The regression yielded the following result: Estimated(EARN) = 239.16 + 5.20(Age) , R = 0.05, SER = 287.21 Standard errors are reported as hereunder: SE(intercept) = (20.24) SE(Age) = (0.57) (a) Is the relationship between "Age" and "EARN" statistically significant? (b) Explain the meaning of heterskedasticity. Is there any reason to be concerned about heteroskedasticity in this model? Briefly explain your reasons. (c) Construct a 95% confidence interval for the slope coefficient, and use it to test for the statistical significance of the slope coefficient. (d) Construct a 95% confidence interval for the intercept coefficient, and use it to test for the statistical significance of the intercept coefficient.Data is collected from a sample of 1,000 US households in an attempt to understand the relationship between income and money spent eating out at restaurants. A regression is estimated based on the data, and the equation is as follows: Spending; 10.12 + 0.25 * Income; + 756.48 * City: 122.96 * Children where restaurant spending and income are yearly values measure in $, city is a binary variable that takes on a 1 if the household lives in a city, and children is the number of children in the family. What is the predicted restaurant spending for a household with a yearly income of $50,000, not located in a city, and with 3 children? $12,387.16 $12,141.24 $12,131.12 $12,897.72A website that rents movies online recorded the age and the number of movies rented during the past month for some of their customers. The data are shown below for a random sample of 25 of their customers.The regression line for the data, with number of movie rentals as the response variable, provides an intercept = 18.87, and slope = -0.228. The standard error of the slope SE(b1) = 0.0827. Margin of error ME for a 99% Confidence Interval for the slope of the Population regression line is: 0.1161 0.2322 0.4644 0.3483
- Interpret the coefficients in the regression modelA researcher wants to test the relationship between the number of years of formal education received (X) and the average weekly earnings (Y) (measured in hundred dollars). A report released by a government agency suggests that the average weekly earnings of individuals with no formal education is equal to $545. The researcher wants to test whether the average weekly earnings with no formal education is $545 or greater than that. He collects data from a sample of 120 individuals and estimates the following regression function: Y-6.91+2.30X, (1.25) (4.25) where , is the predicted value of the weekly earnings for the individual and the standard errors for the coefficients appear in parenthesis. The f-statistic for the test the researcher wants to conduct will be (Round your answer to two decimal places)Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables