2. A Corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict their eventual success. The accompanying table records average weekly sales (in thousands of dollars) and aptitude test scores from a random sample of eight representatives. Test Weekly Sales Score 10 55 12 60 28 85 24 75 18 80 16 85 15 65 12 60 a. Estimate the linear regression of weekly sales on aptitude test scores. b. Interpret the estimated slope of the regression line. c. Test the null hypothesis that representatives' weekly sales are not linearly related to their aptitude test scores against the alternative that there is positive association.

2. A Corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict their eventual success. The accompanying table records average weekly sales (in thousands of dollars) and aptitude test scores from a random sample of eight representatives. Test Weekly Sales Score 10 55 12 60 28 85 24 75 18 80 16 85 15 65 12 60 a. Estimate the linear regression of weekly sales on aptitude test scores. b. Interpret the estimated slope of the regression line. c. Test the null hypothesis that representatives' weekly sales are not linearly related to their aptitude test scores against the alternative that there is positive association.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?
Mumbai Electronics is planning to extend its marketing region from the western United States to include the midwestern states. In order to predict its sales in this new region, the company has asked you to develop a linear regression of DVD system sales on price, using the following data supplied by the marketing department: Sales 418 384 343 407 432 386 444 427 Price 98 194 231 207 89 255 149 195 a. Use an unbiased estimation procedure to find an estimate of the variance of the error terms in the population regression. b. Use an unbiased estimation procedure to find an estimate of the variance of the least squares estimator of the slope of the population regression line. c. Find a 90% confidence interval for the slope of the population regression line.
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Show that an interaction term of a dummy variable and a regressor changes the slope of a regression line..
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A corporation administers an aptitude test to all new sales representatives.Management is interested in the extent to which this test is able to predict their eventual success. The accompanying table records average weekly sales (in thousands of pesos) and aptitude test scores for a random sample of eight representatives. TEST SCORES WEEKLY SCORE 55 10 60 12 85 28 75 24 80 18 85 16 65 15 60 12 1. Plot a scatter diagram2. Estimate the linear regression of weekly sales on aptitude test scores.3. Estimate the weekly sales when test scores is 704. Determine the coefficient of…
If the correlation coefficient is zero, the slope of a linear regression line will be a. positive b. negative c. positive or negative
In a simple linear regression model with one predictor variable, what is the coefficient of determination (R-squared) if the Pearson's correlation coefficient between the predictor and response variable is 0.6?
Seven North American Green Frogs (Rana clamitans) had their jumping distance recorded (in mm) multiple times in a laboratory. The mean jumping distance for these frogs along with their length (measured from snout to vent in miMillimeters) are presented in the table below. Length of Frog 52 68 37 65 77 81 59 Mean Jumping Distance 546 673 415 659 793 814 563 (a) Determine the linear regression model that will best predit the mean jumping distance of a North American Green Frog based on the frog's length. (b) How well does the linear regression model fit this sample data? (c) Use the linear regression model to predict the mean jumping distance of a North American Green Frog that is 48 mm in length. No excel, please.
A corporation administers an aptitude test to all new sales representatives.Management is interested in the extent to which this test is able to predict theireventual success. The accompanying table records average weekly sales (inthousands of pesos) and aptitude test scores for a random sample of eightrepresentatives. TEST SCORES WEEKLY SALES 55 10 60 12 85 28 75 24 80 18 85 16 65 15 60 12 1. Plot a scatter diagram2. Estimate the linear regression of weekly sales on aptitude test scores.3. Estimate the weekly sales when test scores is 704. Determine…
Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 What is the predicted area of a kitchen with a height of 96 inches and 10 cabinets? Report your answer to 1 decimal place. square feet