Researchers at a car resale company are trying to build a model to predict a car’s 4-year resale value (in thousands of dollars) from several predictor variables. The variables theyselected follow.a) What is the equation of the least-squares regression line? A particular car (not atruck) cost $40,000 and has an engine of 3.8 liters. What do you predict the 4-year resalevalue of this car will be?b) Use α = 0.05 to test the significance of β1. Should x1 be dropped from the model?c) Test if there exists any linear relationship between the dependent variable and anyof the independent variables, i.e., test H0 : B1=B2=B3= 0 at 5% significance level. Model1EngineData were collected on cars of different models made by different manufacturers. SPSSoutput for the least-squares regression model is given below.Model1Model1R.962RegressionResidualTotal(Constant)TypePriceEngineModel:TypePriceModel SummaryR Square.9260 if the vehicle is a car 1 if the vehicle is atruckThe price of the vehicle in thousands ofdollarsThe size of the engineSum ofSquares df14568.64231170.761 11515739.404 118BANOVA897643.874-1.893AdjustedR Square.924UnstandardizedCoefficientsCoefficientsMean SquareStd. Error,900717.028.386Std. Error ofthe Estimate3.191FSig4856.214 477.010 .00010.18195% Confidence Interval for BLower Bound Upper Bound-.8852.6792.064930-1.129-.777.817-2.658Y₁ = Bo + B₁ X₁1 + B₂ X2i + B3 X31 + EiwhereY₁ = 4-year resale value, X₁1 = Type, X₂i = Price, X31 = EngineBased on the SPSS output, answer the following questions:

Researchers at a car resale company are trying to build a model to predict a car’s 4- year resale value (in thousands of dollars) from several predictor variables. The variables they selected follow. a) What is the equation of the least-squares regression line? A particular car (not a truck) cost $40,000 and has an engine of 3.8 liters. What do you predict the 4-year resale value of this car will be? b) Use α = 0.05 to test the significance of β1. Should x1 be dropped from the model? c) Test if there exists any linear relationship between the dependent variable and any of the independent variables, i.e., test H0 : B1=B2=B3= 0 at 5% significance level.

Researchers at a car resale company are trying to build a model to predict a car’s 4- year resale value (in thousands of dollars) from several predictor variables. The variables they selected follow. a) What is the equation of the least-squares regression line? A particular car (not a truck) cost $40,000 and has an engine of 3.8 liters. What do you predict the 4-year resale value of this car will be? b) Use α = 0.05 to test the significance of β1. Should x1 be dropped from the model? c) Test if there exists any linear relationship between the dependent variable and any of the independent variables, i.e., test H0 : B1=B2=B3= 0 at 5% significance level.

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

See similar textbooks

Similar questions

A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef(SE) CoefT-ValueP-Value Constant 105.086.0017.510.000 Foot length 2.5990.23810.920.000 S=5.90181R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. BoldItalicUnderlineSuperscriptSubscriptUndoRedoΩBullet listNumbered listImage (12 image limit) Edit imageView imageDelete image Question 2 (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. BoldItalicUnderlineSuperscriptSubscriptUndoRedoΩBullet listNumbered listImage (12 image limit) Edit imageView imageDelete…
The materials handling manager of a manufacturing com-pany is trying to forecast the cost of maintenance for thecompany’s fleet of over-the-road tractors. The manager be-lieves that the cost of maintaining the tractors increases withtheir age. The following data was collected: a. Use POM for Windows’ least squares-linear regressionmodule to develop a relationship to forecast the yearlymaintenance cost based on the age of a tractor.b. If a section has 20 three-year-old tractors, what is the fore-cast for the annual maintenance cost?
A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE) Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. (c) The following histogram summarizes the 65 residuals. Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer.…
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE) Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) The following histogram summarizes the 65 residuals. Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer. (b) Based on your answer to part (a), would it be surprising to randomly select a high school senior from the high school with a foot length of 20cm and a height greater than 165cm? Justify your answer.
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE)Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm.
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE) Coef T-value P-value Constant 105.08 6.00 17.51 0.000 Foot Length 2.599 0.238 10.92 0.000 S=5.90181 R-sq= 65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. (c) The following histogram summarizes the 65 residuals. Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation5.9cm. What percent of the residuals are greater than 8cm? Justify your answer. (d) Based on your answer to part (c), would…
A company trains its employees with instructional videos and claims that the amount of time, in hours, spent training is linearly related to an increase in productivity. The company selected a random sample of five employees to test its claim. The data were used to create the computer output for a least-squares linear regression, shown in the table. Variable DF Estimate SE Intercept 1 3.6 1.1489 Hours 1 0.8 0.3464 Which of the following is the correct test statistic and number of degrees of freedom? t=2.31 with 4 degrees of freedom A t=2.31 with 3 degrees of freedom B t=2.31 with 5 degrees of freedom C t=3.13 with 1 degree of freedom D t=3.13 with 3 degrees of freedom E
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data is Yi=−1.068+1.394Xi and the standard error of the estimate is SYX=19.412. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Significance level at 0.05 . Complete parts (a) and (b) below.
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data is Yi=−1.606+1.428Xi and the standard error of the estimate is SYX=19.348. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Complete parts (a) and (b) below. a. At the 0.01 level of significance, is there evidence of a linear relationship between online trailer views and opening weekend box office gross? Determine the hypotheses for the test. b. Construct a 95%confidence interval estimate of the population…
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data isYi=−0.914+1.408Xi and the standard error of the estimate is SYX=19.887. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Compute the test statistic.