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The Red Book is an Australian company that provides valuation information on the wholesale and retail prices of cars. Taking a random sample of used cars for sale from their database, sampling only for the same model and manufacture year of car, it is possible to model the relationship between the price of car (measured in thousands of dollars) and the number of kilometers it has been driven (measured in thousands of kilometers). A least squares (LS) estimation is applied to estimate the regression model and some summary statistics are shown in the following table. mean var COV sum of squares sample size (n) sum of squared residuals table intercept slope Use this information to answer all the questions below. (a) Fill the blanks in the regression table. estimate [a] Kilometers ('000s) 100.64 54.99 20.66 896084.17 88.00 598.38 [e] s.e. [b] [f] Price ($,000s) 65.96 14.64 t [c] [g] p-value [d] [h] In your answer, you may arrange the values as in the above output table or simply write [a]=XXX, ..., [h]=XXX. (b) What is the value of R2 (R-squared)

The Red Book is an Australian company that provides valuation information on the wholesale and retail prices of cars. Taking a random sample of used cars for sale from their database, sampling only for the same model and manufacture year of car, it is possible to model the relationship between the price of car (measured in thousands of dollars) and the number of kilometers it has been driven (measured in thousands of kilometers). A least squares (LS) estimation is applied to estimate the regression model and some summary statistics are shown in the following table. mean var COV sum of squares sample size (n) sum of squared residuals table intercept slope Use this information to answer all the questions below. (a) Fill the blanks in the regression table. estimate [a] Kilometers ('000s) 100.64 54.99 20.66 896084.17 88.00 598.38 [e] s.e. [b] [f] Price ($,000s) 65.96 14.64 t [c] [g] p-value [d] [h] In your answer, you may arrange the values as in the above output table or simply write [a]=XXX, ..., [h]=XXX. (b) What is the value of R2 (R-squared)

Linear Algebra: A Modern Introduction
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 Red Book is an Australian company that provides valuation information on the wholesale and retail prices of cars. Taking a random sample of used cars for sale from their database, sampling only for the same model and manufacture year of car, it is possible to model the relationship between the price of car (measured in thousands of dollars) and the number of kilometers it has been driven (measured in thousands of kilometers). A least squares (LS) estimation is applied to estimate the regression model and some summary statistics are shown in the following table. mean var COV table intercept slope sum of squares sample size (n) sum of squared residuals Use this information to answer all the questions below. (a) Fill the blanks in the regression table. estimate [a] Kilometers ('000s) 100.64 54.99 20.66 896084.17 88.00 598.38 [e] s.e. [b] [f] Price ($, 000s) 65.96 14.64 t [c] [g] p-value [d] [h] In your answer, you may arrange the values as in the above output table or simply write [a]=XXX, ..., [h]=XXX. (b) What is the value of R² (R-squared)
Transcribed Image Text:The Red Book is an Australian company that provides valuation information on the wholesale and retail prices of cars. Taking a random sample of used cars for sale from their database, sampling only for the same model and manufacture year of car, it is possible to model the relationship between the price of car (measured in thousands of dollars) and the number of kilometers it has been driven (measured in thousands of kilometers). A least squares (LS) estimation is applied to estimate the regression model and some summary statistics are shown in the following table. mean var COV table intercept slope sum of squares sample size (n) sum of squared residuals Use this information to answer all the questions below. (a) Fill the blanks in the regression table. estimate [a] Kilometers ('000s) 100.64 54.99 20.66 896084.17 88.00 598.38 [e] s.e. [b] [f] Price ($, 000s) 65.96 14.64 t [c] [g] p-value [d] [h] In your answer, you may arrange the values as in the above output table or simply write [a]=XXX, ..., [h]=XXX. (b) What is the value of R² (R-squared)
(c) What is the underlying null hypothesis for B₁ (beta_1) from the t-statistic in the Table of question (a)? (d) What is the underlying alternative hypothesis for ₁ (beta_1) from the p-values in the Table of question (a)? (e) Compute the 90% confidence interval for B₁ (beta_1) and explain its interpretation. Show the steps of calculation. (f) Carry out a test to investigate if low kilometers are associated with high prices at the 1% significance level. You need to (1) define new notation (if any), (2) briefly justify your testing procedure, (3) state the hypotheses, (4) calculate the test statistic and show your calculation steps, (5) use the p-value approach, (6) make decision for the test and briefly explain.
Transcribed Image Text:(c) What is the underlying null hypothesis for B₁ (beta_1) from the t-statistic in the Table of question (a)? (d) What is the underlying alternative hypothesis for ₁ (beta_1) from the p-values in the Table of question (a)? (e) Compute the 90% confidence interval for B₁ (beta_1) and explain its interpretation. Show the steps of calculation. (f) Carry out a test to investigate if low kilometers are associated with high prices at the 1% significance level. You need to (1) define new notation (if any), (2) briefly justify your testing procedure, (3) state the hypotheses, (4) calculate the test statistic and show your calculation steps, (5) use the p-value approach, (6) make decision for the test and briefly explain.
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