Ch 8-9 Review: Correlation and Regression

All but one of these statements contain a blunder. Which could be true?

• The correlation between a football player’s weight and the position he plays is 0.54.

• The correlation between the amount of fertilizer used and the yield of beans is 0.42.

• The correlation between a car’s length and its fuel efficiency is 0.71 miles per gallon.

• There is a high correlation (1.09) between height of a corn stalk and its age in weeks.

• There is a correlation of 0.63 between gender and political party.

Residuals are . . .

• possible models not explored by the researcher.

• variation in the data that is explained by the model.

• the difference between observed responses and values predicted by the model.

• data collected from individuals that is not consistent with the rest of the group.

• none of these.

Which statement(s) about influential points is true?

I. Removal of an influential point changes the regression line.

II. Data points that are outliers in the horizontal direction are more likely to be influential than

points that are outliers in the vertical direction.

III. Influential points have large residuals.

• I only

• I and II

• I and III

• II and III

• I, II, and III

Which is true?

I. Random scatter in the residuals indicates a model with high predictive power.

II. If two variables are very strongly associated, then the correlation between them will be near

+1.0 or -1.0.

III. The higher the correlation between two variables the more likely the association is based in

cause and effect.

• none

• I only

• II only

• I and II only

• I, II, and III

Two variables that are actually not related to each other may nonetheless have a very high correlation because they both result from some other, possibly hidden, factor. This is an example of

• leverage

• a lurking variable

• extrapolation

• regression

• an outlier

Tags

CCSS.HSS.ID.C.9

If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope(b) of the line of best fit and to the correlation(r)?

• both will increase

• both will decrease

• b will increase, and r will decrease

• b will decrease, and r will increase

• both will remain the same

What conditions must be met in order to calculate a correlation? Select all that apply

• Straight enough

• Outlier Condition

• Quantitative variables

• unimodal

• symmetric

What must be examined in order to assess the appropriateness of a linear model? Select all that apply

• The scatterplot must have a linear form

• The scatterplot must have a positive direction

• The scatterplot must have a moderate strength

• the residual plot must be evenly scattered

• the residual plot must be roughly linear

If the correlation is very strong, does this show a cause/effect relationship.

• yes

• no

Will the correlation change if the units are changed or if the variables, x and y, are interchanged?

• yes

• no