A home appraisal company would like to develop a regression model that would predict the selling price of a house based on the age of the house in years (X1), the living area of the house in square feet (X2), and the number of bedrooms (X3). The following regression model was chosen using a data set of house statistics: 88,399554791.3333x231,471.1372x3 The first house from the data set had the following values: Selling price $324,000 Age-22 years Square Feet-2.900 -
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- A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. GPA and Absences 4.8 4.4 4.0 3.6 3.2 2.8 2.4 2.0 1.6 4 6 8 10 12 14 16 Absences (Days) What effect does the circled point have on the standard deviation of the residuals? This point will increase the value of the standard deviation of the residuals because it has a large positive residual. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.…Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub- Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics. Variable Coefficient Standard Error t Statistic 5.4841 Intercept 0.13081 41.92 Sale price -0.0733 0.0234 -3.13 Sub-Zero brand 1.1196 0.1462 7.66 0.06956 0.005351 13.00 Total capacity (in cubic feet) Two-door, freezer on bottom Two-door, side freezer 0.04657 0.08085 0.58 Two-door, freezer on top 0.03596 -9.55 Base -0.3432 -0.7096 -0.8820 One door with freezer 0.1310 -5.42 -5.92 One door, no freezer 0.1491 (a) Write the regression model, being careful to exclude the base indicator variable. (Negative amounts should be indicated by a minus…Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables
- 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 significantYou 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. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.
- Mita, the manufacturer of copiers, has been spending increasing amounts of money on radio and television advertising in recent years. An analyst employed by Mita wanted to estimate a simple linear regression of the company's annual copier sales versus advertising dollars. Th regression results included SSE = 12593 and SSR = 87663. What is the coefficient of determination for this regression? 0.874 0.935 0.144 0.126A 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 the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…
- A finance manager employed by an automobile dealership believes that the number of cars sold in his local market can be predicted by the interest rate charged for a loan. Interest Rate (%) Number of Cars Sold (100s) 3 5 10 7 8 2 The finance manager performed a regression analysis of the number of cars sold and interest rates using the sample of data above. Shown below is a portion of the regression output. Regression Statistics Multiple R0.998868 R2 0.997738 Coefficient |14.88462 Interest Rate -1.61538 Intercept 1. Are there factors other than interest rate charged for a loan that the finance manager should consider in predicting future car sales? 2. Is interest rate charged for a loan the most important factor to be considered in predicting future car sales? Explain your reasoning.The dealership's vice- president of marketing has requested a sales forecast at the prevailing interest rate of 7%. 3. As finance manager, what reasons would you convey to the vice-president in recommending…A 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)1. Data were collected on sales of mountain bikes in 30 sporting goods stores. The regression model was y = total sales (thousands of dollars), *₁ = display floor space (square meters), 2 = competitors' advertising expenditures (thousands of dollars), and x3 = advertised price (dollars per unit). A summary of the regression output is below. Variable (nickname) Intercept FloorSpace Competing Ads Price Coefficient 1225.44 11.52 -6.935 -0.1496 (a) Write the fitted regression equation. Round your coefficient Competing Ads to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. (b-1) Put an X in the correct answer circle. The coefficient of FloorSpace says that each additional square foot of floor space... O adds about 11.52 to sales (in thousands of dollars). takes away 11.52 from sales (in thousands of dollars). O adds about 6.935 to sales (in thousands of dollars). takes away 0.1496 from sales (in thousands of dollars). (b-2) Put an X in the…