Chapter 3 Review

In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was = 10 + 0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

• 85.5

• 90

• 95

• 95.5

The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

• much smaller than 0.52

• much larger than 0.52

• unchanged: equal to 0.52

• slightly smaller than 0.52

• slightly larger than 0.52

All but one of the following statements contains an error. Which statement could be correct?

• There is a correlation of 0.54 between the position a football player plays and his weight.

• We found a correlation of r = –0.63 between gender and political party preference.

• The correlation between the distance travelled by a hiker and the time spent hiking is r = 0.9 meters per second.

• The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.

Which statements below about least-squares regression are correct?

I. Switching the explanatory and response variables will not change the least-squares regression line.

II. The slope of the line is very sensitive to outliers with large residuals.

III. A value of r² close to 1 does not guarantee that the relationship between the variables is linear.

• Only I is correct.

• Only II is correct.

• Only III is correct.

• Both II and III are correct.

• All three statements—I, II, and III—are correct.

There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by predicted height = 50.3 + 6.01(age) where height is measured in centimeters and age in years. Which of the following is not correct?

• The estimated slope is 6.01, which implies that female children between the ages of 5 and 18 increase in height by about 6 cm for each year they grow older.

• The estimated intercept is 50.3 cm. We can conclude from this that the typical height of female children at birth is 50.3 cm.

• The average height of female children when they are 5 years old is about 50% of the average height when they are 18 years old.

• My niece is about 8 years old and is about 115 cm tall. She is taller than average for girls her age.

An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that

• when corn prices are above average, soybean prices also tend to be above average.

• there is almost no relation between corn prices and soybean prices.

• when corn prices are above average, soybean prices tend to be below average.

• when soybean prices go up by 1 dollar, corn prices go up by 70 cents.

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

• The correlation must be 0.

• The correlation must be positive.

• A straight line is not a good model for the data.

• The regression line might or might not be a good model for the data, depending on the extent of the curve.

The fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x is the

• slope of the least-squares regression line.

• correlation

• square of the correlation

• intercept of the least-squares regression line.

Suppose a straight line is fit to data having response variable y and explanatory variable x. Predicting values of y for values of x outside the range of the observed data is called

• causation.

• extrapolation.

• correlation.

• interpolation

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

• amount of rainfall

• the soil