EBK BUSINESS STATISTICS
7th Edition
ISBN: 9780134462783
Author: STEPHAN
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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- We have data from 209 publicly traded companies (circa 2010) indicating sales and compensation information at the firm-level. We are interested in predicting a company's sales based on the CEO's salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to estimate the linear regression sales; = a + ßsalary; + ei and get the following regression results: regress sales salary . Source Model Residual Total sales salary _cons SS 337920405 2.3180e+10 2.3518e+10 df 1 207 208 Coef. Std. Err. .9287785 .5346574 5733.917 1002.477 MS 337920405 111980203 113066454 t Number of obs F(1, 207) Prob> F R-squared Adj R-squared Root MSE P>|t| 1.74 0.084 5.72 0.000 209 3.02 -.1252934 3757.543 0.0838 0.0144 0.0096 10582 [95% Conf. Interval] 1.98285 7710.291 This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary. Suppose a CEO of a company…arrow_forwardFind the least-squares regression line treating square footage as the explanatory variable. y = (Round the slope to three decimal places as needed. Round the intercept to one decimal place as needed.)arrow_forwardWe have data from 209 publicly traded companies (circa 2010) indicating sales and compensation information at the firm-level. We are interested in predicting a company's sales based on the CEO's salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to estimate the linear regression sales; = a + ßsalary; + ei and get the following regression results: . regress sales salary Source Model Residual Total sales salary cons SS 337920405 2.3180e+10 2.3518e+10 df 1 207 208 Coef. Std. Err. .9287785 .5346574 5733.917 1002.477 MS 337920405 111980203 113066454 Number of obs F (1, 207) Prob > F R-squared t P>|t| = Adj R-squared = Root MSE 1.74 0.084 5.72 0.000 = = -.1252934 3757.543 = 209 3.02 0.0838 0.0144 0.0096 10582 [95% Conf. Interval] 1.98285 7710.291 This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary. Interpret the…arrow_forward
- A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?arrow_forwardSuppose Tatiyana is interested in the relationship between language ability and time spent reading. She randomly selects a sample of 30 students from the local high school and collects their scores from a language aptitude test. She surveys the sample asking each student how many hours per month he or she spends reading. Using the sample data, Tatiyana produces a scatterplot with reading time on the horizontal axis and language test scores on the vertical axis. She develops a least squares regression equation where ? is the amount of time spent reading during the month and ?̂ is the predicted value of the language test score. ?̂=3.251x+31.237 Compute the value of ?̂ when a student spends 42 hours reading. Give your answer precise to one decimal place. Avoid rounding until the last step. ?̂= ? points Identify all of the true statements regarding the interpretation of ?̂ when ?=42. The value of ?̂ is ? a. the predicted number of students that read for 42 hours. b. the language test…arrow_forwardAn airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second cityarrow_forward
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