The following data represent the chemistry grades for a random sample of 12 freshmen at acertain college along with their scores on an intelligence test administered while they were stillseniors in high school.Testscore xChemistrygrade y65 50 55 65 55 7076 9065 70 55 70 50 5585 | 748587949881917674а)Obtain the least squares estimates of B, and B and state the estimated regressionfunction.b)Plot the estimated regression function and the data. Does the estimated regressionfunction appear to fit the data well?c)Obtain a point estimate of the chemistry grade which has a test score of 75.What is the point estimate of the change in chemistry grade when test score increase by1 score.d)e)Interpret the regression coefficient

a) Consider a regression function: y=β0+β1x to fit the given data points. Now, we can use the…

Answered: The following data represent the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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The following table shows the percent of water and the number of calories in various canned soups to which 100 g of water are added. (show all the necessary solution) Percent Water in Soups % Water Calories 83.3 28 92.3 26 91.9 39 89.4 57 89.5 57 90.5 36 91.9 32 91.7 32 a. Find the equation of the least squares line for the data. b. Use the equation in part a to find the expected number of calories in a soup that is 87% water. c. Determine the correlation coefficient of the data.
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The following data show the number of hurricanes to directly strike a certain country each decade. A major hurricane is one with a strength rating of 3, 4 or 5. DecadeTotal Number of HurricanesNumber of Major Hurricanes1941 – 195021111951 – 19601881961 – 19701361971 – 19801241981 – 19901551991 – 20001452001 – 200493 Using only completed decades (1941 – 2000), calculate the least squares line for the number of major hurricanes expected based on the total number of hurricanes. (Round your answers to three decimal places.) ŷ = + x
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The table below shows the numbers of bushels of barley cultivated per acre for 12 one-acre plots of land for two different strains of barley, PHT-34 and CBX-21. PHT-34 CBX-21 43 55 49 46 47 43 38 44 47 45 45 49 50 47 46 59 46 52 46 49 45 48 43 51 Determine the minimum data value, the quartiles, and the maximum data value for the PHT-34 and CBX-21 data sets. PHT-34 CBX-21 min Q1 Q2 Q3 max
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Consider the following data. Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer Reports (Vol. 62, No. 4). x 27 47 32 47 23 40 34 52 y 30 22 23 13 29 17 21 14 Given the least squares line = 40.9941 − 0.5263x: (a) Make a residual plot for the least-squares model. Be sure to plot the horizontal line at y = 0. (b) Use the residual plot to comment about the appropriateness of the least squares model for these data. The residuals do not seem to be scattered randomly around the horizontal line at 0. There do not appear to be any outliers.The residuals seem to be scattered randomly around the horizontal line at 0. There do not appear to be any outliers. The residuals do not seem to be scattered randomly around the horizontal line at 0. There do appear to be outliers.The residuals…
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