Question

(v) Why are errors squared in a regression? a. to give more weight to smaller errors b. because summing positive and negative errors will cancel them out c. multiplying positive and negative errors will always result in negative numbers d. errors are not actually squared in a regression   

(vi) The best linear prediction rule is the one that has the least a. error when predicting from the mean. b. squared error when predicting from the mean. c. error when predicting using that rule. d. squared error when predicting using that rule.   

(vii) The sum of the squared errors when predicting from the mean is called a. SSError. b. proportionate reduction in error. c. SSTotal. d. proportion of variance accounted for.   

(viii) What is the formula for the proportionate reduction in error? a. (SSError – SSTotal) / SSError b. (SSError + SSTotal) / SSError c. (SSTotal – SSError) / SSTotal d. SSTotal / (SSError + SSTotal)

(ix) What does it mean when SSTotal minus SSError equals zero? a. This is the best case—it means there is zero error. b. This is the worst case—it means the prediction model has reduced zero error. c. The proportionate reduction in error is 50%. d. The underlying correlation is negative.   

(x) When drawing a regression line for a linear prediction rule, the minimum number of predicted points on a graph that must be located is a. 1. b. 2.   
Homework – Chapter 12. Student name:____________________
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c. 1 if it is a positively sloped line; 2 if it is a negatively sloped line. d. 2 if it is a positively sloped line; 1 if it is a negatively sloped line.   

Answer 1

Solution:

v) Why are errors squared in a regression?

Answer: b. because summing positive and negative errors will cancel them out

The squaring is necessary only to remove any negative signs. It also gives more weights to larger differences.

vi) The best linear prediction rule is the one that has the least

Answer: d. squared error when predicting using that rule.   

This minimizes the amount of variation in the data points from the line.

vii)The sum of the squared errors when predicting from the mean is called

Answer: c.SStotal

The sum of squares of all observation is a measure of how a data set varies around a central number.

viii)What is the formula for the proportionate reduction in error?

Answer:c. (SSTotal – SSError) / SSTotal

ix) What does it mean when SSTotal minus SSError equals zero?

Answer:b. This is the worst case—it means the prediction model has reduced zero error.

x) When drawing a regression line for a linear prediction rule, the minimum number of predicted points on a graph that must be located is

Answer: b. 2