Analyzing Two Variable Relationships

Which of the following is closest to the correlation between the two variables?

• -0.7

• -0.2

• 0.7

• 0.2

Which of the following statements is NOT true of the correlation r between the length in inches and the weight in pounds of a sample of brook trout?

• r must take a value between -1 and 1.

• r is measured in inches.

• If longer trout tend to also be heavier, then r > 0.

• r would not change if we measured the lengths of the trout in centimeters instead of inches.

What effect would removing the point (8.37, 45) have on the regression line?

• Slope would increase; y intercept would increase.

• Slope would increase; y intercept would decrease.

• Slope would decrease; y intercept would increase.

• Slope would decrease; y intercept would decrease.

• The estimated slope is 6.1, which implies that girls in this population between the ages of 5 and 18 are predicted to grow about 6.1 centimeters in heights for each year they grow older.

• The estimated y-intercept is 50.3 centimeters. We can conclude from the intercept that the typical height of girls in this population at birth is 50.3 cm.

• A 10-year-old girl in this population is at least 110.3 cm tall.

• One particular 8-year-old girl is 115 cm tall. She is shorter than expected for girls her age in this population.

• For every 1 degree C increase in temperature, fish activity is predicted to increase by 4.785 units.

• The typical distance of the temperature readings from their mean is about 4.785 degrees C.

• The typical distance of the activity level ratings from the least-squares regression line is about 4.785 units.

• The typical distance of the activity-level ratings from their mean is about 4.785 units.

The percent of the variation in the values of y that is accounted for by the least-squares regression of y on x is

• the correlation.

• the slope of the least-squares regression line.

• the square of the correlation.

• the standard deviation of the residuals.

• No; a negative correlation would allow that conclusion, but this correlation is positive.

• No; the positive correlation might have arisen because seriously ill people go to large hospitals.

• Yes; the positive correlation establishes that a larger hospital size is the reason for longer stays.

• Yes; but only if r is very close to 1.

Two modes were calculated on a set of data, a quadratic model and a linear model. The residual plots for each model is shown. Which of the following statements is supported by these residual plots?

• The linear model is a better fit because there is no pattern in the residuals of the linear model.

• The linear model is a better fit because there is an upside-down, U-shaped pattern in the residuals of the linear model.

• The quadratic model is a better fit because there is no pattern in the residuals of the quadratic model.

• The quadratic model is a better fit because there is a U-shaped pattern in the residuals of the quadratic model.

• -340, 294,317.5

• -100,024,682.5

• 100,024,682.5

• 340, 294,317.5

• active students tend to be students with poor grades and vice versa.

• students with good grades tend to be students who are not involved in many extracurricular activities, and vice versa

• students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extra curricularactivities

• there is no linear relationship between number of activities and grade point average for students at this school