Concept explainers
Making Predictions. In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10-5 on page 493. Use a 0.05 significance level.
8. Best Supporting Actors and Actresses For 30 recent Academy Award ceremonies, ages of Best Supporting Actors (x) and ages of Best Supporting Actresses (y) are recorded. The 30 paired ages yield
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- ev The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, y = bo + b₁x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 28 33 36 42 45 Number of Bids 1 7 8 9 10 Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Table Copy Data Nextarrow_forwardExplain whether each scenario below is a regression, classification, or unsupervised learn- ing problem. If it is a supervised learning scenario, indicate whether we are more interested in inference or prediction. Finally, provide in each case the number of observations, n, and the number of predictors, p. (1) An online retailer must decide whether to display advertisement A or advertisement B to each customer on the basis of collected customer demographics (age, income, zip code, and gender). A set of 150 of its customers have already expressed a preference for one advertisement or the other. (2) A policy analyst is interested in discovering factors that are associated with the crime rate across different U.S. cities. For each of 500 cities, the policy analyst gathers the following data: the crime rate, unemployment rate, population, median income, median home price, and state. (3) The the channel owner to see where the subscribers are located, their age and gender, the times and days…arrow_forwardThe accompanying table shows the percentage of employment in STEM (science, technology, engineering, and math) occupations and mean annual wage (in thousands of dollars) for 16 industries. The equation of the regression line is 31.218x +45.915. Use these data to construct a 95% prediction interval for the mean annual wage (in thousands of dollars) when the percentage of employment in STEM occupations is 14% in the industry. Interpret this interval. E Click the icon to view the mean annual wage data. Construct a 95% prediction interval for the mean annual wage (in thousands of dollars) when the percentage of employment in STEM occupations is 14% in the industry.arrow_forwardA magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. Click the icon to view the table of summated ratings and cost per person. ..... a. Construct a scatter plot. Choose the correct graph below. A. Ов. С. D. ACost ($) 90- ACost ($) 90- ACost ($) 90- ACost ($) 90- 0- 0- 90 90 90 90 Rating Rating Rating Rating b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b, and b,. bo = and b, (Round to two decimal places as needed.) c. Interpret the meaning of the Y-intercept, bo, and the slope, b,. Choose the correct answer below. O A.…arrow_forwardA magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. Click the icon to view the table of summated ratings and cost per person. a. Construct a scatter plot. Choose the correct graph below. O A. Ов. OC. OD. ACost ($) 90- Q A Cost ($) 904 A Cost ($) 90- ACost ($) 90- 0- 0- 0- 0- 90 Rating 90 Rating 90 90 Rating Rating Summated ratings and cost per person b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and b,. bo =D and b, =O (Round to two decimal places as needed.) Summated Rating Cost ($ per person)|9 c. Interpret the…arrow_forwardA magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. Click the icon to view the table of summated ratings and cost per person. a. Construct a scatter plot. Choose the correct graph below. O A. 90+ 0 0 Cost ($) The M Rating 90 Q O B. A Cost (5) 90+ 0 H +4 Alpe Rating 90 Q b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and b₁. bo= and b₁ = (Round to two decimal places as needed.) C O C. 90+ 0- Cost (S) HA Rating 90 Q Summated Ratings and Cost Per Person Summated Rating Cost ($ per person) 40 48 60 61 42 40 43 55 67 69…arrow_forwardIt is a model that shows or predict the relationship between two variables. A. Linear Regression B. Correlation Coefficient C. Statistics D. Cryptographyarrow_forwardInterpreting a Computer Display. In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the StatCrunch display and answer the given questions or identify the indicated items. The display is based on Data Set 5 “Family Heights” in Appendix B. Height of Son A son will be bom to a father who is 70 in. tall and a mother who is 60 in. tall. Use the multiple regression equation to predict the height of the son. Is the result likely to be a good predicted value? Why or why not?arrow_forwardDetermine the statistical test that should be conducted before conducting linear regression? a. Normality test b. Variance Homogeneity test c. Correlation d. Data transformationarrow_forwardUse correlation coefficients to determine which of the given sets of data is best fit by its associated regression line and which is fit worst. a. ((6, 8), (3, 14), (7, 6)) b. ((5, 6), (6,5), (7, 6)) c. ((5, 5), (10, 0), (7, 7.1)) Select the data set with the best fit. O ((6, 8), (3, 14), (7, 6)) ((5, 6), (6, 5), (7, 6)) ((5, 5), (10, 0), (7, 7.1)) Select the data set with the worst fit. O ((6, 8), (3, 14), (7, 6)) ((5, 6), (6, 5), (7, 6)) ((5, 5), (10, 0), (7, 7.1)) Is it a perfect fit for any of the data sets? Yes Noarrow_forwardHeptathlon 2004 again We saw the data for the wom-en’s 2004 Olympic heptathlon in Exercise 63. Are the two jumping events associated? Perform a regressionof the long-jump results on the high-jump results.a) What is the regression equation? What does the slopemean?b) What percentage of the variability in long jumps canbe accounted for by high-jump performances?c) Do good high jumpers tend to be good long jumpers?d) What does the residuals plot reveal about the model?e) Do you think this is a useful model? Would you useit to predict long-jump performance? (Compare theresidual standard deviation to the standard deviationof the long jumps.)arrow_forwardFive pairs of data are used in determining a regression line ŷ = -3 + 4x. If the five values of the explanatory variable are 28, 45, 16, 41, and 20, respectively, what is the mean of the five values of the response variable?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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