Question 1

Write the transformed regression equation. Make sure to define any variables used in your
equation.

Accepted Answer

The answer of Write the transformed regression equation. Make sure...

Question 2

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?
A) 5'
B) 11'
C) 83'
D) 19'
E) 93'

Accepted Answer

The answer of It's easy to measure the circumference of...

Question 3

A company's sales increase by the same amount each year. This growth is . . .
A) exponential
B) linear
C) logarithmic
D) power
E) quadratic

Accepted Answer

Linear growth means that the increase is the same amount each year.

Question 4

Use your equation to predict the cost of a 48" stop sign.

Accepted Answer

The answer of Use your equation to predict the cost...

Question 5

All but one of these statements contain a mistake. Which could be true?
A) There is a high correlation (1.09) between height of a corn stalk and its age in weeks.
B) There is a correlation of 0.63 between gender and political party.
C) The correlation between the amount of fertilizer used and the yield of beans is 0.42.
D) The correlation between a car's length and its fuel efficiency is 0.71 miles per gallon.
E) The correlation between a football player's weight and the position he plays is 0.54.

Accepted Answer

Correlation values range from -1 to 1. A correlation of 0.42 between fertilizer and bean yield is plausible, while other options either exceed the possible range or incorrectly apply correlation to categorical data.

Question 6

If the point in the upper right corner of this scatterplot is removed from the data set, then what will
Happen to the slope of the line of best fit (b) and to the correlation (r)? 
A) b will increase, and r will decrease.
B) both will remain the same.
C) both will increase.
D) both will decrease.
E) b will decrease, and r will increase.

Accepted Answer

The answer of If the point in the upper right...

Question 7

Residuals are . . .
A) none of these
B) the difference between observed responses and values predicted by the model.
C) possible models not explored by the researcher.
D) data collected from individuals that is not consistent with the rest of the group.
E) variation in the data that is explained by the model.

Accepted Answer

Residuals are the differences between the observed values and the values predicted by a model, indicating the error in the predictions.

Question 8

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.
A) I, II, and III
B) I and III
C) II and III
D) I only
E) I and II

Accepted Answer

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

Question 9

Breaking strength A company manufactures polypropylene rope in six different sizes. To
assess the strength of the ropes they test two samples of each size to see how much force
(in kilograms) the ropes will hold without breaking. The table shows the results of the tests.
We want to create a model for predicting the breaking strength from the diameter of the
rope.
a. Find a model that uses re-expressed data to straighten the scatterplot.
b. The company is thinking of introducing a new 25mm rope. How strong should it be?
(Write a sentence in context based on one of your models.)

Accepted Answer

The answer of Breaking strength A company manufactures polypropylene rope...

Question 10

Use the equation $\log ($ difftemp $) = 2.057 - 0.025$ time to predict the difference in temperature at time 0 minutes. What does this value represent?

Accepted Answer

The answer of Use the equation $\log ($ difftemp \()...

Question 11

Two variables that are actually not related to each other may nonetheless have a very high
Correlation because they both result from some other, possibly hidden, factor. This is an example of
A) a lurking variable.
B) an outlier.
C) leverage.
D) extrapolation.
E) regression.

Accepted Answer

A lurking variable is a hidden factor that affects both variables, causing them to appear correlated when they are not directly related.

Question 12

Use the equation log(  $=2.057-0.025 \text { time }$
 
to predict the difference in temperature
after 45 minutes.

Accepted Answer

The answer of Use the equation log(  \(=2.057-0.025 \text...

Question 13

A scatterplot of $\frac { 1 } { \sqrt { y } }$ vs. x shows a strong positive linear pattern. It is probably true that
A) large values of X are associated with large values of Y.
B) the scatterplot of Y vs X also shows a linear pattern.
C) the residuals plot for regression of Y on X shows a curved pattern.
D) the correlation between X and Y is near +1.0.
E) accurate predictions can be made for Y even if extrapolation is involved.

Accepted Answer

If the scatterplot of $\frac { 1 } { \sqrt { y } }$ vs. x shows a strong positive linear pattern, it suggests that the relationship between Y and X is not linear, and transforming Y was necessary to achieve linearity. Therefore, the residuals plot for regression of Y on X would likely show a curved pattern, indicating non-linearity.

Question 14

Interpret R-sq in the context of this problem.

Accepted Answer

The answer of Interpret R-sq in the context of this...

Question 15

Another company's sales increase by the same percent each year. This growth is . . .
A) linear
B) power
C) logarithmic
D) exponential
E) quadratic

Accepted Answer

Exponential growth occurs when a quantity increases by a constant percentage each year, leading to a multiplicative effect over time.

Question 16

Describe why performing linear regression with these data is not a good decision.

Accepted Answer

The answer of Describe why performing linear regression with these...

Question 17

Which is true?
I. Random scatter in the residuals indicates a model with high predictive power.
II. If two variables are very strongly associated, then the correlation between them will be near +1.0
Or -1.0.
III. The higher the correlation between two variables the more likely the association is based in
Cause and effect.
A) I only
B) none
C) I, II, and III
D) II only
E) I and II

Accepted Answer

The answer of Which is true?
I. Random scatter in the...

Question 18

Write the equation of the least-squares regression line for the transformed data. Draw the
regression line on the scatterplot in question 2.

Accepted Answer

The answer of Write the equation of the least-squares regression...

Question 19

Newton's Law of Cooling suggests an exponential function is appropriate. Re-express the
data using logarithms and sketch a new scatterplot.

Accepted Answer

The answer of Newton's Law of Cooling suggests an exponential...

Question 20

Do you think this transformation for linearity was successful? Why?

Accepted Answer

The answer of Do you think this transformation for linearity...

Quiz 8: Regression, Associations, and Predictive Modeling

Write the transformed regression equation. Make sure to define any variables used in your equation.

A company's sales increase by the same amount each year. This growth is . . .

Use your equation to predict the cost of a 48" stop sign.

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

If the point in the upper right corner of this scatterplot is removed from the data set, then what will Happen to the slope of the line of best fit (b) and to the correlation (r) ?

Residuals are . . .

Use the equation $\log ($ difftemp $) = 2.057 - 0.025$ time to predict the difference in temperature at time 0 minutes. What does this value represent?

Two variables that are actually not related to each other may nonetheless have a very high Correlation because they both result from some other, possibly hidden, factor. This is an example of

Use the equation log( $Use the equation log( =2.057-0.025 \text { time } to predict the difference in temperature after 45 minutes.$ $=2.057-0.025 \text { time }$ to predict the difference in temperature after 45 minutes.

A scatterplot of $\frac { 1 } { \sqrt { y } }$ vs. x shows a strong positive linear pattern. It is probably true that

Interpret R-sq in the context of this problem.

Another company's sales increase by the same percent each year. This growth is . . .

Describe why performing linear regression with these data is not a good decision.

Write the equation of the least-squares regression line for the transformed data. Draw the regression line on the scatterplot in question 2.

Newton's Law of Cooling suggests an exponential function is appropriate. Re-express the data using logarithms and sketch a new scatterplot.

Do you think this transformation for linearity was successful? Why?

Quiz 8: Regression, Associations, and Predictive Modeling

Write the transformed regression equation. Make sure to define any variables used in your equation.

A company's sales increase by the same amount each year. This growth is . . .

Use your equation to predict the cost of a 48" stop sign.

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

If the point in the upper right corner of this scatterplot is removed from the data set, then what will Happen to the slope of the line of best fit (b) and to the correlation (r) ?

Residuals are . . .

Use the equation log⁡(\log (log( difftemp )=2.057−0.025) = 2.057 - 0.025)=2.057−0.025 time to predict the difference in temperature at time 0 minutes. What does this value represent?

Two variables that are actually not related to each other may nonetheless have a very high Correlation because they both result from some other, possibly hidden, factor. This is an example of

Use the equation log( =2.057−0.025 time =2.057-0.025 \text { time }=2.057−0.025 time to predict the difference in temperature after 45 minutes.

A scatterplot of 1y\frac { 1 } { \sqrt { y } }y​1​ vs. x shows a strong positive linear pattern. It is probably true that

Interpret R-sq in the context of this problem.

Another company's sales increase by the same percent each year. This growth is . . .

Describe why performing linear regression with these data is not a good decision.

Write the equation of the least-squares regression line for the transformed data. Draw the regression line on the scatterplot in question 2.

Newton's Law of Cooling suggests an exponential function is appropriate. Re-express the data using logarithms and sketch a new scatterplot.

Do you think this transformation for linearity was successful? Why?

Use the equation $\log ($ difftemp $) = 2.057 - 0.025$ time to predict the difference in temperature at time 0 minutes. What does this value represent?

Use the equation log( $Use the equation log( =2.057-0.025 \text { time } to predict the difference in temperature after 45 minutes.$ $=2.057-0.025 \text { time }$ to predict the difference in temperature after 45 minutes.

A scatterplot of $\frac { 1 } { \sqrt { y } }$ vs. x shows a strong positive linear pattern. It is probably true that