1. In a multipleregression problem involving two independent variables, if b 1 i
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Question
1. In a multipleregression problem involving two independent variables, ifb1 is computed to be +2.0, it means that
A) the estimated average ofY increases by 2 units for each increase of 1 unit ofX1, holding X2constant.
B) the relationship betweenX1 and Y is significant.
C) the estimated average ofY is 2 when X1 equals zero.
D) the estimated average ofY increases by 2 units for each increase of 1 unit ofX1, without regard toX2.
2. The coefficient ofmultiple determinationr2Y.12
A) measures the proportion ofvariation in Y that is explained by X1and X2.
B) measures the variation aroundthe predicted regression equation.
C) measures the proportion ofvariation in Y that is explained by X1holding X2 constant.
D) will have the same sign asb1.
3. In a multipleregression model, which of the following is correct regarding thevalue of the adjusted r2?
A) It can be larger than 1.
B) It can be negative.
C) It has to be larger than thecoefficient of multiple determination.
D) It has to be positive.
4. The variationattributable to factors other than the relationship between theindependent variables and the explained variable in a regressionanalysis is represented by
A) error sum of squares.
B) regression mean squares.
C) regression sum ofsquares.
D) total sum of squares.
Explanation / Answer
1) A. Looking at the predicted output, we see that a unitincrease in x1 results in an increase in y of b1. This occursbecause we are using a LINEAR regression. 2) A. The correlation coefficient tells you how well theregression fits the data. In other words, how much of thevariation in y can be explained by the variation in the predictivefactors. 3) B. Adjusted R^2 penalizes you for adding factors that donot explain the variation in y and thus can be negative. 4) A. SSE is the sum of square errors between the regressionand actual data.
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