Joe ran a regression. He wants to estimate if the value of properties (EMV_Total
ID: 3340925 • Letter: J
Question
Joe ran a regression. He wants to estimate if the value of properties (EMV_Total) can be determined using the commute duration (DriveTime) and the age of the Building. He obtained the following tables.
What can you tell us about that table? (5 Points)
What is the determination coefficient? (1 point) How does it differ from the correlation coefficient? (2 Points)
Joe is telling you that because the correlation coefficient is .8, he assumes that 80% of the dependent variable (EMV_Total) can be explained by the independent variable. Why is he wrong (2 Points)
What is the difference between the tStat, and the P-Value? Why are they important? (5 Points)
What are the assumed testing hypothesis? What does the F Test, T Stat? and P Value tell you? (5 Points)
SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Square standard Error Observations 0.730492 0.533618 0.531687 91595.23 486 ANOVA MS Significance F 2 4.64E+12 2.32E+12 483 4.05E+12 8.39E+09 485 8.69E+12 276.3160825 1.00253E-80 Regression Residual Total Coefficientandard Errt Stat P-value Lower 95% Upper 95% Intercept DRTIME Age -46479.5 14206.91 -3.27161 23883.55 1938.733 12.31915 31087.89 1539.869 20.18866 0.001145874 1.62342E-30 3.59246E-66 -18564.51967 27692.93995 -74394.46679 20074.15555 28062.22057 34113.55887Explanation / Answer
a]
the determination coefficient R^2 = 0.5336 that is 53.36%. and correlation coefficient r = 0.73 ( square root of R^2)
b]
the correlation coefficient is .8, it means there exist a 80% linear relationship between dependent variable (EMV_Total) and independent variable. It does not mean that 80% of the dependent variable (EMV_Total) can be explained by the independent variable. Moreover if coefficient of determination is 80% then we can comment like 80% of the dependent variable (EMV_Total) can be explained by the independent variable.
c]
tStat is the test statistic of regression analysis for testing of intercept = 0 or slope = 0.
and P-value is the probability that finding the observed, or more extreme, results when the null hypothesis (H 0) of a study question is true.
Also P-value is the criteria for checking which hypothesis will be rejected or accepted, and P-value is totally depends on value tStat and its degrees of freedom.
d]
F-test is used for testing the hypothesis that the given regression model is good fit or not. and simultaneously t- test is used for individual parameters are important for model or not.
Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis
2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.