Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.х134101218.001417.35 10.80 17.74 14.7111y 16.11y =+ x (Round to two decimal places as needed.)12.94 17,865.3517.118.26

Regression: In order to obtain the least square regression line, first perform regression analysis…

Answered: Use the given data to find the equation…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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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?
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.
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance Attitute59 7263 6765 7869 8258 7577 8776 9269 8370 8764 78 A. y=11.7+1.02x B. y=2.81+1.35x C. y=−47.3+2.02x D. y=92.3−0.669x
A statistics professor wants to determine how students' final grades are related to mid-term exam scores, applied in the middle of the term, and the number of classes missed. The teacher selects 10 students from his class and obtains the following data as an attachment. Y = b + m1x1 + m2x2 being the general form of the multiple regression equation referring to the data above. Check the alternative that corresponds to the approximate value of b, m1 and m2, respectively: a) 46,39; 0,54; -4,89 b) -4,89; 0,54; 46,39 c) 46,39; -4,89; 0,54 d) -4,89; 46,39; 0,54
The following table gives the data for the grades on the midterm exam and the grades on the final exam. Determine the equation of the regression line, yˆ=b0+b1x�^=�0+�1�. Round the slope and y-intercept to the nearest thousandth. Grades on Midterm and Final Exams Grades on Midterm 7171 6262 7878 9494 8383 8181 8080 9494 8585 6262 Grades on Final 8888 7979 8888 9191 8080 7070 7171 9393 6565 7777
Assume a person got score of 32.5 on Test A and a score of 95.25 on Test B. Using the regression equation (B' = 2.3A + 9.5), what is the error of prediction for this person?
If the coefficient of determination is 0.86 with corresponding regression line ˆy=2x+10, what is the correlation coefficient? (Hint: r is the correlation coefficient and must have the same sign as the slope of the regression line) (i) 0.9274 (ii) -0.9274 (iii) -0.7396 (iv) 0.0726
A study was done that examined the effectiveness of a 7-Minute Screen test for Alzheimer’s disease. The study evaluated the relationship between scores from the 7-Minute Screen and scores for the same patients from a set of cognitive exams that are typically used to test for Alzheimer’s disease. For a sample of n=9 patients, the scores for the 7-Minute Screen averaged M=7 with SS = 92. The cognitive test scores averaged M=17 with SS = 236. For these data, SP = 127. Find the regression equation for predicting the cognitive scores from the 7-Minute Screen score. b = a = Regression equation = What percentage of variance in the cognitive scores is accounted for by the regression equation? r = r2 = Does the regression equation account for a significant portion of te variance in the cognitive scores? Use α = .05 to evaluate the F ratio. MSregression = MSresidual = Fcalculated = Fcritical = Decision =
A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.586 Stdev width: 0.877 Mean height: 13.037 Stdev height: 1.697 Correlation coefficient: 0.7814 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
If 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 +0.97
For the 2011 season, suppose the average number of passing yards per attempt for a certain NFL team was 6.1. Use the estimated regression equation developed in part (c) to predict the percentage of games won by that NFL team. (Note: For the 2011 season, suppose this NFL team's record was 7 wins and 9 losses. Round your answer to the nearest integer.)
The personnel director of a large hospital is interested in determining the relationship (if any) between an employee’s age and the number of sick days the employee takes per year. The director randomly selects ten employees and records their age and the number of sick days which they took in the previous year. Employee 1 2 3 4 5 6 7 8 9 10Age 30 50 40 55 30 28 60 25 30 45Sick Days 7 4 3 2 9 10 0 8 5 2 The estimated regression equation and the standard error are given. Sick Days=14.310162−0.236900(Age) Se=1.682207 Find the 95% prediction interval for the average number of sick days an employee will take per year, given the employee is 34 . Round your answer to two decimal places.

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