Asked by Kaitlin Ptacek on Jun 07, 2024
Verified
A professor of economics wants to study the relationship between income (y in $1000s) and education (x in years). A random sample eight individuals is taken and the results are shown below. Determine the standard error of estimate.
sr = ______________
Describe what this statistic tells you about the regression line.
____________________________
Determine the coefficient of determination.
R2 = ______________
Discuss what its value tells you about the two variables.
________________________________________________________
Calculate the Pearson correlation coefficient.
r = ______________
Why does it have the sign it has?
________________________________________________________
Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.
Test statistic:
t = ______________
Rejection Region:
Reject H0 if | t | > ______________
Conclusion:
______________
A linear relationship ______________ between years of education and income.
Standard Error Of Estimate
A measure of the accuracy of predictions made with a regression line, specifically, it estimates the standard deviation of the error term.
Coefficient Of Determination
A measure used in statistical analysis to assess the goodness of fit of a model, represented as the proportion of variance in the dependent variable that is predictable from the independent variable(s).
Pearson Correlation Coefficient
A measure of the linear correlation between two variables X and Y, giving a value between -1 and 1 which indicates the strength and direction of the correlation.
- Ascertain and expound upon the standard error of estimate together with the standard error of the slope.
- Master the concepts and calculation methods for the coefficient of determination.
- Calculate and interpret the coefficient of correlation.
Verified Answer
Learning Objectives
- Ascertain and expound upon the standard error of estimate together with the standard error of the slope.
- Master the concepts and calculation methods for the coefficient of determination.
- Calculate and interpret the coefficient of correlation.
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