Question 1

Which statement about influential points is true?
I. Removal of an influential point changes the regression line.
II. Data points that are outliers in the horizontal direction are more likely to be influential than
Points that are outliers in the vertical direction.
III. Influential points have large residuals.

Accepted Answer

Influential points affect the regression line significantly when removed (I). Horizontal outliers are more likely to be influential (II). However, influential points do not necessarily have large residuals (III).

Question 2

Variables X and Y have $r = 0.40$ 0.40. If we decrease each X value by 0.1, double each Y value, and then
Interchange them (put X on the Y-axis and vice versa) the new correlation will be

Accepted Answer

The correlation coefficient $r$ is unaffected by changes in scale or location of the variables, so the correlation remains 0.40.

Question 3

R-sq is a measure of ...

Accepted Answer

R-sq, or R-squared, measures the proportion of the variability in the response variable that is explained by the explanatory variable in a regression model.

Question 4

If a data point is influential it…

Accepted Answer

An influential data point is one that significantly affects the slope of the regression equation, often because it is extreme in the horizontal direction.

Question 5

Suppose we collect data hoping to be able to estimate the prices of commonly owned new cars (in
$) from their lengths (in feet). Of these possibilities, the slope of the line of best fit is most likely to
Be

Accepted Answer

The answer of Suppose we collect data hoping to be...

Question 6

Which of the following is not a source of caution in regression between two variables?

Accepted Answer

All of these options are potential problems in regression analysis, as they can affect the validity and reliability of the results.

Question 7

The relationship between the number of hours a person practices a task and the time it takes them
To complete the task is calculated to have R $\mathrm { R } - \mathrm { sq } = 56.7 \%$
) The value of the correlation coefficient is

Accepted Answer

The answer of The relationship between the number of hours...

Question 8

A regression model examining the amount of distance a long distance runner runs (in miles) to
Predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is
Appropriate?

Accepted Answer

The slope of 4.6 indicates that for every additional mile run, the runner is predicted to drink 4.6 more ounces of fluid.

Question 9

All but one of the statements below contain a mistake. Which one could be true?

Accepted Answer

Correlations range from -1 to 1, and they do not have units. A correlation of -0.36 between golf score and practice hours is plausible, indicating a weak negative relationship.

Question 10

A regression analysis of students' AP* Statistics test scores and the number of hours they spent
Doing homework found $r ^ { 2 } = 0.32$
0)32 . Which of these is true?
I. 32% of student test scores can be correctly predicted with this model.
II. Homework accounts for 32% of your grade in AP* Stats.
III. There's a 32% chance that you'll get the score this model predicts for you.

Accepted Answer

The $r^2$ value of 0.32 indicates that 32% of the variability in test scores can be explained by the number of hours spent on homework, not that 32% of scores can be predicted, that homework accounts for 32% of the grade, or that there's a 32% chance of getting the predicted score.

Question 11

An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the
circumference of a plate by using the diameter in inches. Their model is chee^rios = 0.56 + 5.11(diameter).
-If the diameter is increased from 4 inches to 14 inches, the predicted number of cheerios will
Increase by about…

Accepted Answer

The increase in the number of cheerios is calculated by the change in diameter multiplied by the coefficient of the diameter in the model: 5.11 * (14 - 4) = 5.11 * 10 = 51.

Question 12

A medical researcher finds that the more overweight a person is, the higher his pulse rate tends to
Be) In fact, the model suggests that 12-pound differences in weight are associated with differences
In pulse rate of 4 beats per minute. Which is true?
I. The correlation between pulse rate and weight is 0.33
II. If you lose 6 pounds, your pulse rate will slow down 2 beats per minute.
III. A positive residual means a person's pulse rate is higher than the model predicts.

Accepted Answer

The answer of A medical researcher finds that the more...

Question 13

This regression analysis examines the relationship between the number of years of formal
Education a person has and their annual income. According to this model, about how much more
Money do people who finish a 4-year college program earn each year, on average, than those with
Only a 2-year degree? Dependent variable is Income
R-squared $= 25.8 \%$
$\mathrm { s } = 3888$ with 57 degrees of freedom
$\begin{array} { l c c } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } \ \text { Constant } & 3984.45 & 6600 \ \text { Education } & 2668.45 & 600.1 \end{array}$

Accepted Answer

The coefficient for Education is $2668.45, which represents the average increase in income for each additional year of education. The difference between a 4-year and a 2-year degree is 2 years, so the increase in income is $2 \times 2668.45 = 5336.9$, approximately $5337.

Question 14

Computer output in the scenario described in problem #8 reports that $s = 2.3 .$ . Which is the correct
Interpretation of this value?

Accepted Answer

The value $s = 2.3$ represents the standard deviation of the residuals, which is the average prediction error of the regression line.

Question 15

Although there are annual ups and downs, over the long run, growth in the stock market averages
About 9% per year. A model that best describes the value of a stock portfolio is probably:

Accepted Answer

The stock market's average growth of about 9% per year suggests a consistent percentage increase, which is characteristic of exponential growth.

Question 16

When using midterm exam scores to predict a student's final grade in a class, the student would
Prefer to have a

Accepted Answer

A positive residual indicates that the actual final grade is higher than the predicted grade, which is preferable for the student.

Question 17

A correlation of zero between two quantitative variables means that

Accepted Answer

A correlation of zero indicates that there is no linear relationship between the two variables, but there could still be a non-linear association.

Question 18

A scatterplot of log(Y) vs. log(X) reveals a linear pattern with very little scatter. It is probably true That …

Accepted Answer

The answer of A scatterplot of log(Y) vs. log(X) reveals...

Question 19

It's easy to measure the circumference of a tree's trunk, but not so easy to measure its height.
Foresters developed a model for ponderosa pines that they use to predict the tree's height (in feet)
From the circumference of its trunk (in inches): ln $\hat { h } = - 1.2 + 1.4 ( \ln C )$
) ) A lumberjack finds a tree
With a circumference of 60"; how tall does this model estimate the tree to be?

Accepted Answer

To find the estimated height, substitute C = 60 into the model: ln(ĥ) = -1.2 + 1.4(ln(60)). Calculate ln(60), multiply by 1.4, add -1.2, and then exponentiate to find ĥ. The result is approximately 93 feet.

Question 20

If a data set has a relationship that is best described by a linear model, than the residual plot will

Accepted Answer

A residual plot with no pattern and a correlation near 0 indicates that a linear model is appropriate for the data set, as it suggests that the residuals are randomly distributed around the horizontal axis.

Quiz 2: Exploring Relationships Between Variables

Variables X and Y have $r = 0.40$ 0.40. If we decrease each X value by 0.1, double each Y value, and then Interchange them (put X on the Y-axis and vice versa) the new correlation will be

R-sq is a measure of ...

If a data point is influential it…

Suppose we collect data hoping to be able to estimate the prices of commonly owned new cars (in $) from their lengths (in feet) . Of these possibilities, the slope of the line of best fit is most likely to Be

Which of the following is not a source of caution in regression between two variables?

The relationship between the number of hours a person practices a task and the time it takes them To complete the task is calculated to have R $\mathrm { R } - \mathrm { sq } = 56.7 \%$ ) The value of the correlation coefficient is

A regression model examining the amount of distance a long distance runner runs (in miles) to Predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is Appropriate?

All but one of the statements below contain a mistake. Which one could be true?

Computer output in the scenario described in problem #8 reports that $s = 2.3 .$ . Which is the correct Interpretation of this value?

Although there are annual ups and downs, over the long run, growth in the stock market averages About 9% per year. A model that best describes the value of a stock portfolio is probably:

When using midterm exam scores to predict a student's final grade in a class, the student would Prefer to have a

A correlation of zero between two quantitative variables means that

A scatterplot of log(Y) vs. log(X) reveals a linear pattern with very little scatter. It is probably true That …

If a data set has a relationship that is best described by a linear model, than the residual plot will

Quiz 2: Exploring Relationships Between Variables

Variables X and Y have r=0.40r = 0.40r=0.40 0.40. If we decrease each X value by 0.1, double each Y value, and then Interchange them (put X on the Y-axis and vice versa) the new correlation will be

R-sq is a measure of ...

If a data point is influential it…

Suppose we collect data hoping to be able to estimate the prices of commonly owned new cars (in $) from their lengths (in feet) . Of these possibilities, the slope of the line of best fit is most likely to Be

Which of the following is not a source of caution in regression between two variables?

The relationship between the number of hours a person practices a task and the time it takes them To complete the task is calculated to have R R−sq=56.7%\mathrm { R } - \mathrm { sq } = 56.7 \%R−sq=56.7% ) The value of the correlation coefficient is

A regression model examining the amount of distance a long distance runner runs (in miles) to Predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is Appropriate?

All but one of the statements below contain a mistake. Which one could be true?

Computer output in the scenario described in problem #8 reports that s=2.3.s = 2.3 .s=2.3. . Which is the correct Interpretation of this value?

Although there are annual ups and downs, over the long run, growth in the stock market averages About 9% per year. A model that best describes the value of a stock portfolio is probably:

When using midterm exam scores to predict a student's final grade in a class, the student would Prefer to have a

A correlation of zero between two quantitative variables means that

A scatterplot of log(Y) vs. log(X) reveals a linear pattern with very little scatter. It is probably true That …

If a data set has a relationship that is best described by a linear model, than the residual plot will

Variables X and Y have $r = 0.40$ 0.40. If we decrease each X value by 0.1, double each Y value, and then Interchange them (put X on the Y-axis and vice versa) the new correlation will be

The relationship between the number of hours a person practices a task and the time it takes them To complete the task is calculated to have R $\mathrm { R } - \mathrm { sq } = 56.7 \%$ ) The value of the correlation coefficient is

Computer output in the scenario described in problem #8 reports that $s = 2.3 .$ . Which is the correct Interpretation of this value?