80* DeltaMathItamath.com/app/student/solve/14923198/linearRegressionLinear RegressionsDec 16, 3:58:59 PMWatch help videoA mathematics teacher wanted to see the correlation between test scores andhomework. The homework grade (x) and test grade (y) are given in the accompanyingtable. Write the linear regression equation that represents this set of data, roundingall coefficients to the nearest tenth. Using this equation, estimate the homeworkgrade, to the nearest integer, for a student with a test grade of 87.Homework Grade (x) Test Grade (y)779988889422837109847373Copy Values for Calculator000000DDLA

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Answered: A mathematics teacher wanted to see the…

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 17HP

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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?
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
In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation as ˆ y = 14 + 0.5 x y ^ = 14 + 0.5 x where y is the final-exam score and x is the score on the first test. Andrea scored 75 on the first test. What is the predicted value of the Andrea's score on the final exam? Andrea scored 56.5 on the final exam. What is the value of the residual?
Disk drives last time Here is a scatterplot of the residu-als from the regression of the hard drive prices on their sizes from Exercise 18.a) Are any assumptions or conditions violated? If so,which ones?b) What would you recommend about this regression?
The least-squares regression equation is y=647.8x+17,858 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7507. predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. Round to the nearest dollar as needed.
We recorded the pre-statistics course grade (in percent) and introductory statistics course grade (in percent) for 60 community college students. In this data set, no one earned a 90% for the pre-statistics course grade. How could you estimate a student’s introductory statistics course grade if she earned 90% for the pre-statistics course grade? A. Substitute 90 into the regression equation: Predicted introductory statistics course grade = -0.147 + 0.981(90) . B. Substitute the decimal 0.90 into the regression equation: Predicted introductory statistics course grade = -0.147 + 0.981(0.90).
The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.
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.)
33. Ramon wants to better understand the relationship between income and hours of sleep, so he performs a regression analysis using sleep as the independent variable and income as the dependent variable. The result is a regression line with an equation of y = 4,500x+13,562 and r = .75. Based off of this result, can we conclude that sleeping more leads to a higher income? Group of answer choices No, a correlation of .75 is not high enough to make this conclusion. Yes, a correlation of .75 is high enough to make this conclusion. No, we cannot determine causality from regression analysis, only associations. Yes, a positive slope indicates that more sleep leads to higher incomes
A researcher found a linear correlation between course grades and the average number of hours spent on a mobile phone each day. The line of best fit has equation y ^ = 3.7 − 0.786 x with correlation coefficient r = − 0.84. a. Does this prove that spending too much time on a phone causes students to get lower grades? b. What does the regression line predict your final grade in a course will be if you spend an average of 150 minutes per day on your phone?
Use your graphing utility’s linear regression option to obtain a model of the form y = ax + b that fits the data. How well does the correlation coefficient, r, indicate that the model fits the data?
A group of scientists are interested in finding out whether the days of rainfall during the dry season could predict the magnitude of butterfly migration in the local area during wet season. Every year for twenty years, they count the total days of rainfall during the dry season preceding the migration and measure the number of butterflies migrating in the following wet season. Which type of statistical test should they use to analyze their data? (pearson's r correlation OR, simple regression equation)

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