Question 1. True (T) or False (F)? (a) Let Y and X be a response variable and an

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Question 1. True (T) or False (F)? (a) Let Y and X be a response variable and an explanatory variable, respectively. The model Y- can be fitted by a linear regression model, where and are regression parameters and is a random error. (b) The correlation coefficient between Y and Y is equal to the correlation between Y and X. (c) In a multiple linear regression model Y BoPX+BpXp+E, the absolute values of the t - j-1,2,....p, can be used to check the quality se S.e of the model fit, (d) When several descriptions of the data are available, we should choose a model with the largest R2

Explanation / Answer

(a) False

Linear regression model is always of the form Y = b0 + b1X + E

(b) False

Both the correlation coefficient values will be different.

(c) True

For each coefficient, a t-test is carried out which compares the absolute value of tj with 0 and tells whether the coefficients ane significant or not.

(d) False

R-squared cannot determine whether the coefficient estimates and predictions are biased, which is why you must assess the residual plots.

Also, R-squared does not indicate whether a regression model is adequate. You can have a low R-squared value for a good model, or a high R-squared value for a model that does not fit the data.

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