Relationship Between Two Quantitative Variables

A study of the effects of television measured how many hours of television each of 125 grade school children watched per week during a school year and their reading scores. The study found that children who watch more television tend to have lower reading scores than children who watch fewer hours of television. The study report says, “Hours of television watched explains 25% of the observed variation in the reading scores of the 25 subjects.” The correlation between hours of TV and reading score must be

• r = 0.25

• r = -0.25

• r = -0.5

• r = 0.5

• can’t tell from the given information

If two variables are positively associated, then

• Larger values of one variable are associated with larger values of the other.

• Larger values of one variable are associated with smaller values of the other.

• Smaller values of one variable are associated with larger values of the other.

• Smaller values of one variable are associated with larger and smaller values of the other.

• There is no pattern I the relationship between the two variables.

The correlation coefficient measures

• whether there is a relationship between two variables.

• the strength of the relationship between two quantitative variables.

• whether or not the scatter plot shows an interesting pattern.

• whether a cause and effect relationship exists between the two variables.

• the strength of the linear relationship between two quantitative variables.

Consider the scatter plot, which describes the relationship between stopping distance (in feet) and air temperature (in ℃) for a certain 2000-pound car travelling 40 mph. Do these data provide strong evidence that warmer temperatures cause greater stopping distance?

• Yes. The strong straight-line association in the plot shows that temperature has a strong effect on stopping distance.

• No. r ≠ +1

• No. We can’t be sure temperature is responsible for the difference in stopping distances.

• No. The plot shows that differences among stopping distances are not large enough to be important.

• No. The plot shows that stopping distances go down as temperature increases.

If stopping distance was expressed in yards instead of feet, how would the correlation r between temperatures and stopping distance change?

• r would be divided by 12

• r would be divided by 3

• r would not change

• r would be multiplied by 3

• r would be multiplied by 12

If another point were added with an air temperature of 0 ℃ and a stopping distance of 80 feet, the correlation would

• decrease, since this new point is an outlier that does not follow the pattern of the data.

• increases, since this new point is an outlier that does not follow the pattern of the data.

• stay nearly the same, since correlation is resistant to outliers

• increase, since there would be more data points.

• whether this data point causes an increase or decrease cannot be determined without recalculating the correlation.

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is

• yield of the crop.

• amount of fertilizer applied to the soil.

• the experimenter.

• amount of rainfall.

• the soil.

Which one of the following statements is correct?

• Faculty who are good researchers tend to be poor teachers and vice versa, so the correlation between teaching and research is 0.

• Women tend to be, on average, about 3.5 inches shorter than the men they marry, so the correlation between the heights of spouses must be negative.

• A researcher finds the correlation between the shoe size of children and their score on a reading test to be 0.22. The researcher must have made a mistake since these two variables are clearly unrelated and must have correlation 0.

• If people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive.

• The correlation r equals the proportion of times that two variables lie on a straight-line.

“Least-squares” in the term “least-squares regression line” refers to

• Minimizing the sum of the squares of all values of the explanatory variable.

• Minimizing the sum of the squares of all values of the response variable.

• Minimizing the products of each value of the response variable and the predicted value based on the regression equation.

• Minimizing the sum of the squares of the residuals.

• Minimizing the squares of the differences between each value of the response variable and each value of the explanatory variable.

Which of the following statements concerning residuals is true?

• The sum of the residuals is always 0.

• A plot of the residuals is useful for assessing the fit of the least-squares regression line.

• The value of a residual is the observed value of the response minus the value of the response that one would predict from the least-squares regression line.

• An influential point on a scatter plot is not necessarily the point with the largest residual.

• All of the above.