Question 1

Which statement about re-expressing data is not true?
I.Unimodal distributions that are skewed to the left will be made more symmetric by taking The square root of the variable.
II.A curve in which the direction of the association changes from negative to positive will Not benefit from re-expression.
III.One goal of re-expression may be to make the variability of the response variable more Uniform.
A)I only
B)III only
C)II only
D)II and III
E)I,IIandIII

Accepted Answer

E

Question 2

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)leverage.
B)regression.
C)an outlier.
D)a lurking variable.
E)extrapolation.

Accepted Answer

This is an example of a lurking variable, where an unseen or unconsidered variable influences the relationship between two variables that appear to be correlated, but are not directly causing each other's movement.

Question 3

Which statement about residuals plots is true?
I.A curved pattern indicates nonlinear association between the variables.
II.A pattern of increasing spread indicates the predicted values become less reliable as the
Explanatory variable increases.
III.Randomness in the residuals indicates the model will predict accurately.
A)I only
B)II only
C)I, II, and III
D)I and III only
E)I and II only

Accepted Answer

I and II are correct. A curved pattern in a residuals plot suggests a nonlinear relationship between the variables, indicating that a linear model may not be the best fit. A pattern of increasing spread (heteroscedasticity) suggests that the variance of the error terms increases with the explanatory variable, which can mean the model's predictions become less reliable for larger values of the explanatory variable. III is incorrect because randomness in the residuals indicates that the model has captured the relationship between the variables well, but it does not guarantee accurate predictions for all future observations.

Question 4

A scatterplot of log(Y) vs.log(X) reveals a linear pattern with very little scatter.It is Probably true that …
A)the calculator's LnReg function will model the association between X and Y.
B)the residuals plot for regression of Y on X shows a curved pattern.
C)the correlation between X and Y is near 0.
D)the correlation between X and Y is near +1.
E)the scatterplot of Y vs X shows a linear association.

Accepted Answer

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

Question 5

If a data point is influential it…
A)has a small residual.
B)is guaranteed to be extreme in the vertical direction.
C)is guaranteed to be extreme in the horizontal direction.
D)will change the slope of the regression equation.
E)none of these.

Accepted Answer

An influential data point is one that, when removed, significantly changes the slope of the regression equation. This means it has a strong impact on the line of best fit in a regression analysis.

Question 6

The model$\sqrt{\widehat{\text { distance }}}$  = 3.30 + 0.235 (speed. can be used to predict the stopping distance (in feet. for a car traveling at a specific speed (in mph.) According to this model, about how much distance will a car going $65 \mathrm { mph }$ need to stop?
A) $729.0$ feet
B) $345.0$ feet
C) $27.0$ feet
D) $4.3$ feet
E) $18.6$ feet

Accepted Answer

The answer of The model$\sqrt{\widehat{\text { distance }}}$  =...

Question 7

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, II, and III
B)none
C)I only
D)I and II
E)II only

Accepted Answer

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

Question 8

Which of the following is not a goal of re-expressing data?
A)Make the scatter in a scatterplot spread out evenly rather than following a fan shape.
B)Make the spread of several groups more alike.
C)All of these are goals of re-expressing data.
D)Make the form of a scatterplot more nearly linear.
E)Make the distribution of a variable more symmetric.

Accepted Answer

Re-expressing data aims to make data more suitable for analysis by addressing issues like uneven scatter, differing group spreads, non-linearity, and asymmetry in distributions. Therefore, all the options listed are indeed goals of re-expressing data.

Question 9

A residuals plot is useful because
I.it will help us to see whether our model is appropriate.
II.it might show a pattern in the data that was hard to see in the original scatterplot.
III.it will clearly identify influential points.
A)I and II only
B)I, II, and III
C)II only
D)I only
E)I and III only

Accepted Answer

Residuals plots are useful for diagnosing the fit of a regression model by showing the distribution of the residuals and helping to identify heteroscedasticity or non-linearity, which addresses points I and II. However, while residuals plots can help identify outliers, they do not specifically identify influential points, which are points that have a significant impact on the model's parameters.

Question 10

The $\sqrt { \widehat { s t r } } = 12 + 20 ($ dia $)$ can be used to predict the breaking strength of a rope (in pounds) from its diameter (in inches). According to this model, how much force should a rope onehalf inch in diameter be able to withstand?
A) $16 \mathrm { lbs }$
B) $22 \mathrm { lbs }$
C) $4.7 \mathrm { lbs }$
D) $256 \mathrm { lbs }$
E) $484 \mathrm { lbs }$

Accepted Answer

Substitute the diameter (0.5 inches) into the equation: $\sqrt{\widehat{str}} = 12 + 20(0.5)$. This simplifies to $\sqrt{\widehat{str}} = 22$. Squaring both sides gives $\widehat{str} = 484$ lbs.

Question 11

In predicting the growth of the volume of a small bay by measuring the height of the water at a dock, a researcher is using a model of $\sqrt [ 3 ] { \widehat { volume} } = 2.34 + 4.56$ (height) where height is measured in $\mathrm { m }$ and volume cubic miles. If the height rises to $3.45 \mathrm {~m}$, what is the predicted volume?
A) $2.62 \mathrm {~m} ^ { 3 }$
B) $1.2 \times 10 ^ { 12 } \mathrm {~m} ^ { 3 }$
C) $5902 \mathrm {~m} ^ { 3 }$
D) $7 \times 10 ^ { 7 } \mathrm {~m} ^ { 3 }$
E) $18.1 \mathrm {~m} ^ { 3 }$

Accepted Answer

The answer of In predicting the growth of the volume...

Question 12

Which of the following is not a source of caution in regression between two variables?
A)subgroups with differences
B)extrapolation
C)a lurking variable
D)an outlier
E)all of these are potential problems.

Accepted Answer

All of the options listed (subgroups with differences, extrapolation, a lurking variable, and an outlier) are potential sources of caution or problems in regression analysis between two variables. Each can affect the accuracy of the regression model in different ways, such as skewing the data, introducing bias, or affecting the validity of predictions.

Question 13

Over the past decade a farmer has been able to increase his wheat production by about the Same number of bushels each year.His most useful predictive model is probably…
A)linear
B)logarithmic
C)quadratic
D)exponential
E)power

Accepted Answer

A linear model is most appropriate for situations where there is a constant rate of change, which matches the description of the farmer's wheat production increasing by the same number of bushels each year.

Question 14

A residual plot that has no pattern is a sign that…
A)the original data is straight and the regression line is a good model.
B)the original data is straight and the regression line is not a good model.
C)the model is not a good one, because there is no pattern.
D)the original data is curved and the regression line is not a good model.

Accepted Answer

The answer of A residual plot that has no pattern...

Question 15

Which statement about correlation is true?
I.Regression based on data that are summary statistics tends to result in a higher
Correlation.
II. $\text { If } r = 0.95 , \text { the response variable increases as the explanatory variable increases. }$
III.An outlier always decreases the correlation.

A)I only
B)II only
C)III only
D)I, II, and III
E)none of these

Accepted Answer

Regression based on summary statistics often results in a higher correlation because it reduces variability. Statement II is not necessarily true as correlation does not imply causation, and statement III is false because an outlier can either increase or decrease the correlation depending on its position relative to the data.

Question 16

Another farmer has increased his wheat production by about the same percentage each year.
His most useful predictive model is probably…
A)linear
B)exponential
C)logarithmic
D)quadratic
E)power

Accepted Answer

An exponential model is most appropriate for situations where a quantity increases by a constant percentage each year, which matches the description of the farmer's wheat production.

Question 17

When using midterm exam scores to predict a student's final grade in a class, the student Would prefer to have a
A)negative residual, because that means the student's final grade is lower than we would predict with the model.
B)residual equal to zero, because that means the student's final grade is exactly what we would predict with the model.
C)positive residual, because that means the student's final grade is lower than we would predict with the model.
D)positive residual, because that means the student's final grade is higher than we would predict with the model.
E)negative residual, because that means the students final grade is higher than we would predict with the model.

Accepted Answer

A positive residual indicates that the actual outcome (the student's final grade) is higher than the predicted outcome based on the midterm exam scores. This means the student performed better than expected.

Question 18

Linear regression was used to describe the trend in world population over timE.Below is a
Plot of the residuals versus predicted values.What does the plot of residuals suggest? 
A)An outlier is present in the data set.
B)The linearity condition is not satisfied.
C)A high leverage point is present in the data set.
D)The data are not normal.

Accepted Answer

The answer of Linear regression was used to describe the...

Quiz 8: Regression Wisdom

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

If a data point is influential it…

The model $\sqrt{\widehat{\text { distance }}}$ = 3.30 + 0.235 (speed. can be used to predict the stopping distance (in feet. for a car traveling at a specific speed (in mph.) According to this model, about how much distance will a car going $65 \mathrm { mph }$ need to stop?

Which of the following is not a goal of re-expressing data?

A residuals plot is useful because I.it will help us to see whether our model is appropriate. II.it might show a pattern in the data that was hard to see in the original scatterplot. III.it will clearly identify influential points.

The $\sqrt { \widehat { s t r } } = 12 + 20 ($ dia $)$ can be used to predict the breaking strength of a rope (in pounds) from its diameter (in inches) . According to this model, how much force should a rope onehalf inch in diameter be able to withstand?

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

Over the past decade a farmer has been able to increase his wheat production by about the Same number of bushels each year.His most useful predictive model is probably…

A residual plot that has no pattern is a sign that…

Which statement about correlation is true? I.Regression based on data that are summary statistics tends to result in a higher Correlation. II. $\text { If } r = 0.95 , \text { the response variable increases as the explanatory variable increases. }$ III.An outlier always decreases the correlation.

Another farmer has increased his wheat production by about the same percentage each year. His most useful predictive model is probably…

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

Linear regression was used to describe the trend in world population over timE.Below is a Plot of the residuals versus predicted values.What does the plot of residuals suggest?