Concept explainers
The following is the ANOVA summary table for a multiple regression model with two independent variables:
a. determine whether there is a significant relationship between
b. compute the coefficients of partial determination,
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardFor the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracyarrow_forwardFor the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.arrow_forward
- For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.arrow_forwardThe local utility company surveys 12 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis is as follows: bill = 16.2 + 3.58. size. Coefficients Estimate Std. Error (Intercept) 16.2 Size 3.58 0.47 0.68 Round your answer to three decimal places, and round any interim calculations to four decimal places. We are 99% confident that the mean annual electric bill increases by between dollars for every additional square foot in home size. dollars andarrow_forwardAs a marketing manager for TriFood, you want to determine whether store Sales (# sold in one month) of TriPower bars are related to price (in cents) of TriPower bars and in-store promotional expenditures (in dollars) for TriPower bars. You conduct a multiple regression analysis with store Sales (Y) as the response variable, and Price (X1) and Promotion (X2) as explanatory variables. Use the pictured Excel regression output below to answer the questions. a) Interpret the value for R square. Interpret the estimated coefficient for price. b) State the hypotheses for assessing the statistical significance of the overall regression equation. Does the model overall fit the data (yes or no?) f) An external consultant to TriFoods believes that for every $1 increase in promotional expenditures, sales will increase by 4.7 units. Test the consultant's hypothesis at a 5% significance level using both approaches (tcalc vs tcrit and p-value vs a).arrow_forward
- As a marketing manager for TriFood, you want to determine whether store Sales (# sold in one month) of TriPower bars are related to price (in cents) of TriPower bars and in-store promotional expenditures (in dollars) for TriPower bars. You conduct a multiple regression analysis with store Sales (Y) as the response variable, and Price (X1) and Promotion (X2) as explanatory variables. Use the pictured Excel regression output below to answer the questions. a) Write the estimated multiple regression equation. b) Should one interpret the estimated value for the intercept (yes or no)? c) Interpret the value for Standard Error under Regression Statistics. d) Interpret the value for R square. e) State the hypotheses for assessing the statistical significance of the overall regression equation. f) Interpret the estimated coefficient for price. g) An external consultant to TriFoods believes that for every $1 increase in promotional expenditures, sales will increase by 4.7 units. Test the…arrow_forwardThe sweetness, y, of the fruit is supposed to be related to the average daily sunshine hours, x. The following data shows the sweetness of the same type of fruit at different locations (sunshine hours). Fit the data to a simple linear regression model. x: 5, 6, 7, 6, 6, 8, 7, 5. y: 9, 10, 10, 11, 12, 13, 12, 8. Predict the true mean sweetness for average daily hours of 8 hours, and calculate the residual for average daily sunshine hours of 8 hours.arrow_forwardA vending machine company operates coffee vending machines in office buildings. The company wants to study the relationship between the number of cups of coffee sold per day and the number of persons working in each building. Data were collected were collected by the company and presented below. Number of Number of Cups of f. Make a copy of the scatter diagram in this item. Draw the line that best fits in the scatter diagram using the regression equation. persons Coffee Sold working at Location g. Locate the (X,). Describe its location in relation to the other plotted data. 15 20 10 15 h. Give a practical interpretation of the values of a and b. 16 20 i. Show that the regression equation can be expressed in the form: (y - y) = b(x - x) 18 25 22 30arrow_forward
- Is the number of calories in a beer related to the number of carbohydrates and/or the percentage of alcohol in the beer? The accompanying table has data for 35 beers. The values for three variables are included: the number of calories per 12ounces, the alcohol percentage, and the number of carbohydrates (in grams) per 12 ounces. a. Perform a multiple linear regression analysis, using calories as the dependent variable and percentage alcohol and number of carbohydrates as the independent variables. Let X1 represent alcohol percentage and let X2 represent the number of carbohydrates. (Round to four decimal places as needed.)arrow_forwardUsing the lengths (in.), chest sizes (in.), and weights (lb) of bears from a data set, the resulting regression equation is Weight=-274 +0.426 Length + 12.1 Chest Size. The P-value is 0.000 and the adjusted R² value is 0.925. If an additional predictor variable of neck size (in.) is included, the P-value becomes 0.000 and the adjusted R² becomes 0.933. Why is it better to use values of adjusted R² instead of simply using values of R²? Choose the correct answer below. C O A. The unadjusted R² can only be calculated for regression equations with two or fewer predictor variables, while the adjusted R² can be calculated for regression equations with any number of predictor variables. O B. The unadjusted R² increases or remains the same as more variables are included, but the adjusted R² is adjusted for the number of variables and sample size. OC. The unadjusted R² can only be calculated for regression equations with P-values greater than 0, while the adjusted R² can be calculated for…arrow_forwardUsing the lengths (in.), chest sizes (in.), and weights (lb) of bears from a data set, the resulting regression equation is Weight= -274 +0.426 Length + 12.1 Chest Size. The P-value is 0.000 and the adjusted R² value is 0.925. If an additional predictor variable of neck size (in.) is included, the P-value becomes 0.000 and the adjusted R² becomes 0.933. Why is it better to use values of adjusted R² instead of simply using values of R²? Choose the correct answer below. C O A. The unadjusted R² can only be calculated for regression equations with P-values greater than 0, while the adjusted R² can be calculated for regression equations with any manner of P-value. O B. The unadjusted R² increases or remains the same as more variables included, but the adjusted R² is adjusted for the number of variables and sample size. OC. The unadjusted R² decreases or remains the same as more variables are included, but the adjusted R² is adjusted for the number of variables and sample size. O D. The…arrow_forward
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