A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 76. Homework Grade (x) Test Grade (y) 61 52 54 52 86 76 77 69 53 51 77 62 90 85 Copy Values for Calculator Open Statistics Calculator

A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 76. Homework Grade (x) Test Grade (y) 61 52 54 52 86 76 77 69 53 51 77 62 90 85 Copy Values for Calculator Open Statistics Calculator

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 2ECP

See similar textbooks

Similar questions

Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
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?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown in the excel worksheet. Find the regression equation
The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.
The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive? Is the regression coefficient statistically significant? How can you tell?
A car dealer wants to estimate the price of a used car based on the age of the car and the mileage. Based on a sample of 20 cars, she determines the sample regression equation that predicts price taxes on the basis of the age (in years) of the number of miles is Price=21,619-1022Age-0.03 Miles (a) If the age of the car was fixed and the mileage was increased by 10,000, how much would the price increase or decrease and by how much? (b) Predict the selling price of a five-year-old car with 65,000 miles. (Round your answers to the nearest whole number.)
In a simple linear regression analysis, the correlation coefficient (r) and the slope (b) ___________ have the same sign?
Assume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment?
A company has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents (Y). Analysis on the set finds that the regression equation is Y=60-0.5*X. What can be said of the correspondence (relation) between age and accidents? Are younger workers safer or more prone to accident? What is the likely number of accidents for someone aged 25?
In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 17 wines, a model was created using the percentages of alcohol to predict wine quality. From the results of that regression, b1=0.4386 and Sb1=0.1141. a. At the 0.05 level of significance, is there evidence of a linear relationship between the percentage of alcohol and wine quality? b. Construct a 95% confidence interval estimate of the population slope, β1. b. The 95% confidence interval is __ ≤ β1 ≤ __ (Round to three decimal places as needed.)
A college bookstore must order books two months before each semester starts. They believe that the number of books that will ultimately be sold for any particular course is related to the number of students registered for the course when the books are ordered. They would like to develop a linear regression equation to help plan how many books to order. From past records, the bookstore obtains the number of students registered, X, and the number of books actually sold for a course, Y, for 12 different semesters. These data are below. Show the complete table for your solutions. At a .01 level of significance is there sufficient evidence to conclude that the number of books sold is related to the number of registered students in a straight-line manner? Calculate df:Indicate whether it is a one-tail or two-tail test:Use the table for PEARSON'S CORRELATION COEFFICIENT r (Critical Values):Make a Decision by comparing critical r with the computer Pearson Correlation Coefficient: