Simple Linear Regression - Relationship Between Variables
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Answer the following questions:
a) If r^2 = 0.95, n = 11 and the ∑ (y − y) 2 = 100, what is S (2 -- e) or S^2 yx ?
b) If r^2 = 1, then S (2 -- e) in (1a) can be shown to have what type of relationship with SST and SSR?
c) What relationship exists between y-hat and Y where r^2 = 1?
d) What relationship exists between y-hat and Y where r^2 = 0?
e) Given the following information: r^2 = 0.95, n = 10 and k =2 what is the t-value for b1?
f) In (e), you calculated t-value at the 0.05 level of significance; what statistical decision can you make about b1?
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The solution discusses various problems in simple linear regression analysis in an attached word document.
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Solution
We have r^2 = 1 - sum of (y_i - y-hat)^2/ sum of (y_1 - y-bar)^2
= 1 - ...
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