General Studies · Linear Regression
Let {(xi, yi); i = 1, 2, ..., n} be given data points, where not all xi values are the same. C decides to fit a linear regression model of y on x with an intercept, and D decides to fit a linear regression model of y on x without an intercept. Let x̄ and ȳ be the sample means of x and y respectively. Which of the following statements regarding the two fitted models is NOT necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Both the fitted regression lines will pass through the point (x̄, ȳ)✓
- 2C's fitted line will pass through (x̄, ȳ), but D's fitted line may not pass through (x̄, ȳ)
- 3For C's fitted model, the sample correlation coefficient between xi and the corresponding residuals is zero
- 4The sum of residuals for C's fitted model is always zero
Correct answer
Both the fitted regression lines will pass through the point (x̄, ȳ)
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