How is grit related to an individual's overall personal achievement, which includes income, happiness, health, family and friendship? A government agency has conducted a survey on a simple random sample of individuals on grit and summarised an achievement index for them. A least squares (LS) estimation is applied to estimate the regression model E (Achievement, | Grit,) = + PGrit, Some summary statistics are shown in the following table.
How is grit related to an individual's overall personal achievement, which includes income, happiness, health, family and friendship? A government agency has conducted a survey on a simple random sample of individuals on grit and summarised an achievement index for them. A least squares (LS) estimation is applied to estimate the regression model E (Achievement, | Grit,) = + PGrit, Some summary statistics are shown in the following table.
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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![How is grit related to an individual's overall personal achievement, which includes income,
happiness, health, family and friendship? A government agency has conducted a survey on a simple
random sample of individuals on grit and summarised an achievement index for them.
A least squares (LS) estimation is applied to estimate the regression model
E (Achievement, | Grit,) = Bo + B Grit,
Some summary statistics are shown in the following table.
Grit
Achievement
mean
64.86
34.87
var
456.3
70.10
Cov
165.76
sum of squares
409942
sample size (n)
88
sum of squared residuals 859.65
Use the information to answer all the questions below.
(a) Fill the blanks in the regression table.
table
estimate
s.e.
p-value
intercept
[a]
[b]
[c]
[d]
slope
[e)
(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 R?
(c) What is the underlying null hypothesis for ß, from the t-statistic in the Table of question (a)?
(d) What is the underlying alternative hypothesis for Bi from the p-values in the Table of question
(a)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bc354e2-153e-42b1-a1d6-3db19cb7db7a%2F33ff6777-ea60-4367-a412-021fe92a1098%2Frw633mc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:How is grit related to an individual's overall personal achievement, which includes income,
happiness, health, family and friendship? A government agency has conducted a survey on a simple
random sample of individuals on grit and summarised an achievement index for them.
A least squares (LS) estimation is applied to estimate the regression model
E (Achievement, | Grit,) = Bo + B Grit,
Some summary statistics are shown in the following table.
Grit
Achievement
mean
64.86
34.87
var
456.3
70.10
Cov
165.76
sum of squares
409942
sample size (n)
88
sum of squared residuals 859.65
Use the information to answer all the questions below.
(a) Fill the blanks in the regression table.
table
estimate
s.e.
p-value
intercept
[a]
[b]
[c]
[d]
slope
[e)
(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 R?
(c) What is the underlying null hypothesis for ß, from the t-statistic in the Table of question (a)?
(d) What is the underlying alternative hypothesis for Bi from the p-values in the Table of question
(a)?
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