AP Statistics Bivariate Vocabulary

The LSRL is fit to a set of data. If one of the data points has a positive residual, then.......

• the correlation between the values of the response and explanatory variables must be positive

• the point must lie above the LSRL

• the point must lie near the right edge of the scatterplot

• the point is probably an influential piont

• all of the above

A study of child development measures the age (in months) at which a child begins to talk and also the child's score on an ability test given several years later. The study asks whether the age at which a child talks helps predict the later test score. The LSRL of test score "y" on age "x" is y-hat=110 - 1.3x. According to this regression line, what happens to children who talk one month later than other children?

• Their predicted test scores go down 110 points

• Their predicted test scores go down 1.3 points

• Their predicted test scores go up 110 points

• Their predicted test scores go up 1.3 points

• Their predicted test scores are 108.7 points

A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in CM) and eg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. (Note: number of eggs is given in 1000's so 40 means 40,000 eggs)

The equation of the LSRL is.......

• eggs = -142.74 + 39.25(length)

• eggs = 39.25 - 142.74(length)

• eggs = 25.55 + 5.932(length)

• length = 25.55 + 5.392(eggs)

• length = -142.74 + 39.25(eggs)

A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in CM) and eg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. (Note: number of eggs is given in 1000's so 40 means 40,000 eggs).

Which of the following statements can be made on the basis of the computer output?

• 83.5% of the variation in egg production can be accounted for by the LSRL of egg production on fish length

• 69.7% of the variation in egg production can be accounted for by the LSRL of egg production on fish length

• 83.5% of the variation in fish length can be accounted for by the LSRL of egg production on fish length

• 69.7% of the variation in fish length can be accounted for by the LSRL of egg production on fish length

• 68.4% of the variation in fish length can be accounted for by the LSRL of egg production on fish length

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 that "Hours of television watched explained 9% of the observed variation in the reading scores of the 125 subjects." The correlation between hours of TV and reading score must be

• r = 0.09

• r = -0.09

• r = 0.3

• r = -0.3

• can't tell from the information given

A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is:

y-hat = 1344 - 19x

On a day when the temperature is 20ºF, the regression line predicts that gas used will be about

• 1724 cubic ft

• 1383 cubic ft

• 1325 cubic ft

• 964 cubic ft

• none of the above

You are examining the relationship between x = the height of red oak trees and y = the number of acorns produced in a five year period. You calculate a correlation coefficient and a least-squares regression line of y on x. If you switched the variables (that is, let x = number of acorns and y = height of trees), which of the following would be true?

• both the correlation coefficient and the regression line would be unchanged

• the correlation coefficient would change, but the regression line would not change

• the correlation coefficient would not change, but the regression line would change

• neither the correlation coefficient nor the regression equation would change

• only the y-intercept fo the regression line would change, the slope of the line and the correlation coefficient would not change.

A simple random sample of 25 world-ranked tennis players provides the following statistics: Number of hours of practice per day: x-bar = 7.3, standard deviation of x = 1.2. Yearly winnings: y-bar = $1,820,000, standard deviation of y = $310,000. Correlation r = .23. Based on this data, what is the resulting linear regression equation?

• predicted winnings = 1,390,000 + 59,400(hours)

• predicted winnings = 1,300,000 + 71,300(hours)

• predicted winnings = -63,400 + 258,000(hours)

• predicted winnings = -443,000 + 310,000(hours)

• predicted winnings = -10,000,000 + 1,620,000(hours)

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model 
y hat = 25.2 + 3.3 x
where x is the number of chirps per minute and is the estimated temperature in degrees Fahrenheit.  Find and interpret the residual in context for the striped ground cricket who chirped 18 chirps per minute while it was 80°F.    

• Residual = 4.6°F.  The temperature was 4.6°F higher than what was expected for a striped ground cricket who chirped 18 chirps per minute.    

• Residual = - 4.6 chirps.  The striped ground cricket chirped 4.6 chirps less than what we expected at the temperature of 80°F.    

• Residual = 4.6 chirps.  The striped ground cricket chirped 4.6 chirps more than what we expected at the temperature of 80°F.    

• Residual =  - 4.6°F.  The temperature was 4.6°F lower than what was expected for a striped ground cricket who chirped 18 chirps per minute.    

• Residual = 20.6°F.  The temperature was 20.6°F higher than what we expected for a striped ground cricket who chirped 18 chirps per minute.      

The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. In this study, the response variable is......

• height of researcher

• volume of lumber

• height of tree

• the measuring instrument used to measure volume

• impossible to determine