Concept explainers
In exercise 7, the data on y = annual sales ($ 1000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation ŷ = 80 + 4x. For these data
- a. Develop a 95% confidence interval for the
mean annual sales for all salespersons with nine years of experience. - b. The company is considering hiring Tom Smart, a salesperson with nine years of experience. Develop a 95% prediction interval of annual sales for Tom Smart.
- c. Discuss the differences in your answers to parts (a) and (b).
Trending nowThis is a popular solution!
Chapter 14 Solutions
Statistics for Business & Economics, Revised (MindTap Course List)
- 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_forwardon the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?arrow_forwardGiven the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?arrow_forward
- Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methodsarrow_forwardMr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the valye of sales ($1000) for each client sampled. Number of Contacts (X) Sales ($1000) 14 24 12 14 20 28 16 30 23 30 a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.arrow_forwardUse the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 – 8.5x3 + 2.2x4 Suppose x2 increased by 2 units. What would be the expected change in x1? Suppose x2 increased by 4 units. What would be the expected change in x1? (e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.454. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit ? upper limit ? (f) Using the information of part (e) and level of significance 10%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t ? t critical ± ?arrow_forward
- A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.arrow_forwardIn exercise 1, the following estimated regression equation based on 10 observations was presented. y^=29.1270+.5906x1+.4980x2Develop a point estimate of the mean value of y when x1=180 and x2=310. Predict an individual value of y when x1=180 and x2=310.arrow_forwardIf the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97arrow_forward
- What is the effect of this violation on the regression model? "The number of observations n is less than or equal to the number of parameters to be estimated"arrow_forwardSuppose the following data were collected from a sample of 15 houses relating selling price to square footage and the architectural style of the house. Use statistical software to find the following regression equation: PRICEi=b0+b1SQFTi+b2COLONIALi+b3RANCHi+ei . Is there enough evidence to support the claim that on average, houses that are ranch style have lower selling prices than houses that are Victorian style at the 0.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."Selling Price Square Footage Colonial (1 if house is Colonial style, 0 otherwise) Ranch (1 if house is Ranch style, 0 otherwise) Victorian (1 if house is Victorian style, 0 otherwise) 377640 1941 1 0 0 460996 3397 0 1 0 405781 2764 0 0 1 407216 2906 0 0 1 435139 3401 1 0 0 405275 2600 0 0 1 381141 2203 0 1 0 370490 2046 1 0 0 404070 2210 0 0 1 460196 3692 0 1 0 382780 2172 1 0 0 406466 2606 0 1…arrow_forwardA paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, µm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.125 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.125 + 0.007x and standard deviation 0.005. (a) What is the mean eggshell thickness for quail eggs that are 15 mm in length? ____ µm What is the mean eggshell thickness for quail eggs that are 17 mm in length? ____ µm (b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.23 µm? _____ (c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.222? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) ____ Approximately what proportion of quail eggs of length…arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill