# R - Multiple regression - Quizz

<quiz display=simple > {The multiple correlation (R) is: (check all that apply)

|type="[]"} +The correlation between predicted and observed scores. -The sum of the simple r's. -The highest simple r. +Always between 0 and 1 (inclusive).

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R is the correlation between predicted and observed scores when there are two or more predictors. It is always between 0 and 1.

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{In multiple regression there are:

|type="[]"} -multiple criterion variables. +multiple predictor variables. -two predictor variables.

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Having two or more predictor variables is what distinguishes multiple regression from simple regression.

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{The difference between a regression weight and a beta weight is:

|type="[]"} -A regression weight assumes linearity. -A beta weight is for the population while a regression weight is for the sample. -A regression weight is less biased. +A beta weight is a standardized regression weight.

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A beta weight is a standardized regression weight.

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{In the regression equation Y' = b1X1 + b2X2 + A, if b1 = 5, then how much would the predicted value of Y differ for two observations that had the same value of X2 but differed by 7 on X1?

|type="{}"} { 35 }

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35

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{The difference between a regression weight and a regression coefficient is: (check all that apply)

|type="[]"} -The regression weight is more important. -The regression weight is unbiased. -The regression weight is added rather than multiplied.

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They are synonymous.

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{A regression weight is a partial slope because:

|type="[]"} +It is the slope when the part of the predictor independent of the other predictors is used to predict the criterion. -It is only one of several slopes, so it is only part of the prediction equation. -It is the relationship between the significant part of a predictor and the criterion. -It is only an estimate of the true slope and so is a partial solution.

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It is the slope when the part of the predictor independent of the other predictors is used to predict the criterion. The other predictors are "partialled out."

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{Find the value of the multiple correlation (R). You should use a computer to find the solution.

Y X1 X2 X3

27.6 1 4 4 9.4 3 5 3 15.6 4 7 1 20.3 5 5 4 12.3 3 7 3 8.7 5 3 6 7.3 7 5 7 14.9 6 4 8 17.0 5 3 9 -0.8 4 2 0

|type="{}"} { 0.7575 }

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0.7575

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{These are the same data as in the previous question. Find the value of b2. You should use a computer to find the solution.

Y X1 X2 X3

27.6 1 4 4 9.4 3 5 3 15.6 4 7 1 20.3 5 5 4 12.3 3 7 3 8.7 5 3 6 7.3 7 5 7 14.9 6 4 8 17.0 5 3 9 -0.8 4 2 0

|type="{}"} { 1.6848 }

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1.6848

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{The sum of squares explained is 200 and the sum of squares error is 100. What is the R2?

|type="{}"} { 0.667 }

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0.667

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{The sum of the simple r2's is typically

|type="[]"} -less than R2 -equal to R2 +greater than R2

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Greater than R squared. Typically there is overlap in the variance explained by the predictors.

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{Which of the following assumptions pertain to inferential statistics in multiple regression?

|type="[]"} -The predictor variables are normally distributed. -The criterion variable is normally distributed. +The errors of prediction (the residuals) are normally distributed. +The variance about the regression line is the same for all predicted values. +The predictor variables are linearly related to the criterion.

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Residuals are normally distributed. The variance about the regression line is the same for all predicted values (homoscedasticity). The predictor variables are linearly related to the criterion.

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