Quiz about AP Stats Chapter 3 Review

Question 1

Which of the following statements about a linear regression model is true?

I. The sum of the residuals is always zero

II. If r²=0, the regression line is a horizontal line.

III. No pattern in the residual plot is an indication that a nonlinear model will show a better fit to the data than a straight-line regression model.

Accepted Answer

I and II only

Answer

I only

Answer

I and III only

Answer

II and III only

Answer

I, II, and III

Question 2

In a statistics course, a linear regression equation was computed to predict the final exam score based on the score on the first test of the term. The equation was y=25+0.7x where y is the final exam score and x is the score on the first test. George scored 80 on the first test. On the final exam George scored 85. What is the value of his residual?

Accepted Answer

4

Answer

-4

Answer

4.5

Answer

5

Answer

81

Question 3

Which of the following statements about correlation, r, are true?

I. When r = 0 , there is no linear relationship between the variables.

II. When r = 0.75, then 75% of the variables are closely related

III. When r = 1, there is a perfect cause and effect relationship between the variables.

Accepted Answer

I only

Answer

II only

Answer

III only

Answer

I and III only

Answer

I, II, and III

Question 4

Which of the following best describes the correlation between two variables if r = 0.987?

Accepted Answer

positive and strong

Answer

negative and weak

Answer

positive and weak

Answer

negative and strong

Answer

no correlation

Question 5

The correlation coefficient is

Accepted Answer

A number between -1 and +1 that measures the strength and direction of the linear relationship between two variables

Answer

always equal to the slope of the regression line

Answer

a positive number that measures the goodness of fit

Answer

never equal to zero

Answer

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

Question 6

The residual plot below came from data which plotted grade at midterm against grade on final exam. A linear regression line was calculated. Which conclusion could be reached by analyzing the residual plot?

Accepted Answer

There exists unequal variance throughout the model.

Answer

Students did better on the final exam than they did on the midterm.

Answer

There is evidence that a linear model is appropriate.

Answer

An exponential curve could be used to predict final grade given midterm grade.

Answer

There is no pattern evident in the residual plot.

Question 7

Question 7.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Answer

E.

Question 8

A student was interested in the relationship between weight of a car and gas consumption measured in mpg. He selected sixteen different automobiles and recorded their weights along with their advertised mpg. The regression equation and regression plot are shown above.

What affect would the addition of the point (4,300 lbs, 15.63 mpg) have on the value of r²?

Accepted Answer

It will increase r² because it is an influential point which lies on the least squares line.

Answer

It will have no effect on r² because it lies on the line.

Answer

It will decrease r² because it is an outlier

Answer

It will increase r² because every additional point will increase the percent variation in y due to the relationship with the lease squares line.

Question 9

The equation of the least squares regression line for a set of points in a scatterplot is given above. The point (5, 7) is one point on this scatterplot. Which of the following is the residual for the point (5, 7)?

Accepted Answer

0.75

Answer

6.25

Answer

4.05

Answer

0.71

Answer

7.87

Question 10

The equation of the least squares regression line for a set of points in a scatterplot is given above. The point (3, 2) is one point on this scatterplot. Which of the following is the residual for the point (3, 2)?

Accepted Answer

-0.11

Answer

0.11

Answer

0.22

Answer

1.04

Answer

1.57

Question 11

Consider the following scatterplots above. What is the relationship between r₁, r₂, and r₃, the correlation coefficients of each scatterplot?

Accepted Answer

r₂< r₁< r₃

Answer

r₁< r₂< r₃

Answer

r₁< r₃< r₂

Answer

r₂< r₃< r₁

Answer

r₃< r₂< r₁

Question 12

For the years 1950-1980, the number of heart disease deaths per 100,000 people in the United States were recorded. The regression line below was computed using a statistical software package. which statement is the correct interpretation of the slope?

The regression equation is

Number of deaths = 7387 - 3.63 year

Accepted Answer

The number of heart disease deaths per 100,000 people has been dropping by an estimated 3.63 deaths per year on the average.

Answer

Heart disease will be cured in the year 2036.

Answer

The regression line estimates that for every 3.63 years there is an average of 1 death due to heart disease per 100,000 people.

Answer

For every 3.63 years there is a decrease on the average of 1 death due to heart disease per 100,000 people.

Answer

There is an increase of approximately 7387 deaths per year.

Question 13

The points (x, y) on a scatterplot form an ellipse. As the ellipse becomes thinner, what can be concluded about the correlation r between the variables x and y?

Accepted Answer

no conclusion can be drawn

Answer

r decreases in absolute value

Answer

r increases in absolute value

Answer

The value of r changes sign.

Answer

r remains constant.

Question 14

Which of the following statements is true?

Accepted Answer

The correlation can be strongly affected by a few outlying observations.

Answer

Changing the measurement units of x and y may affect the correlation between x and y.

Answer

Values of r near 0 indicate a strong linear relationship.

Answer

Strong correlation means that there is a definite cause- and effect relationship between x and y.

Answer

Correlation changes when the x and y variables are reversed.

Question 15

Data obtained from a group of high school seniors comparing age and the number of hours spent on the telephone. The resulting regression equation is

Predicted number of hours = 0.123(age)+2.57 with r =0.866

What percentage of the variation in the number of hours spent on the telephone can be explained by this least-squares regression model?

Accepted Answer

75%

Answer

0.75%

Answer

0.866%

Answer

86.6%

Answer

This value cannot be found with the given information.

Question 16

A linear model was constructed for a set of bivariate data using least squares regression techniques. Given the residual plot shown, what conclusion should be drawn?

Accepted Answer

A linear model was not a good fit for the data.

Answer

A linear model was a good fit for the data.

Answer

The correlation between the original variables is close to 1.

Answer

The data was drawn from a population that was not normally distributed.

Answer

The study was poorly designed.

Question 17

Residuals are

Accepted Answer

the difference between the observed response and the values predicted by the model.

Answer

possible models not explored by the researcher.

Answer

variation in the response variable that is explained by the model.

Answer

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

Answer

a measure of the strength of the linear relationship between x and y.

Question 18

The relationship between the selling price of a car (in $1000) and its age (in years) is estimated from a random sample of cars of a specific model. The relationship is given by the formula above.

Which of the following can be concluded from this equation?

Accepted Answer

For every year the car gets older, the selling price drops by approximately $1182.

Answer

On average, a new car costs about $23,018.

Answer

On average, a new car costs about $11,820.

Answer

For every year the car gets older, the selling price goes down by approximately 11.82%.

Answer

For every year the car gets older, the selling price drops by approximately $2420.

Question 19

A study was done on the relationship between high school GPA and score on the SAT. The following 8 scores sere from a random sample of students taking the exam.