Question 1

All but one of the statements below contain a mistake. Which one could be true?
A) There is a strong correlation between type of preferred pet and income level.
B) The correlation between the height of a bean plant and the day is 0.78 in/day.
C) The correlation between your golf score and the number of hours you practice is -0.36.
D) The correlation between the time it takes to get ready in the morning and gender is 0.78.
E) The number of apricots on a tree and the amount of fertilizer have a 1.12 correlation.

Accepted Answer

The correlation coefficient can range from -1 to 1, with a negative value indicating a negative correlation and a positive value indicating a positive correlation. However, the magnitude of the correlation coefficient cannot exceed 1. Therefore, statements A, B, D, and E are all incorrect because they imply correlation coefficients greater than 1. Statement C could be true because the correlation coefficient can range from -1 to 1, and a correlation coefficient of -0.36 would indicate a weak negative correlation between golf score and practice time.

Question 2

A correlation of zero between two quantitative variables means that
A) re-expressing the data will guarantee a linear association between the two variables.
B) we have done something wrong in our calculation of r.
C) there is no linear association between the two variables.
D) none of these
E) there is no association between the two variables.

Accepted Answer

A correlation of zero indicates that there is no linear association between the two variables, but it does not necessarily mean there is no association at all; non-linear relationships can still exist.

Question 3

It takes a while for new factory workers to master a complex assembly process. During the first month new employees work, the company tracks the number of days they have been on the job and the length of time it takes them to complete an assembly. The correlation is most likely to be
A) near 0
B) exactly -1.0
C) exactly +1.0
D) near -0.6
E) near +0.6

Accepted Answer

Since new employees are still learning the assembly process, we can expect that their productivity will improve over time as they gain experience, which suggests a negative correlation between the number of days on the job and the time to complete an assembly. However, the correlation may not be perfect, as some workers may learn the process more quickly than others, or may have prior experience that helps them adapt more rapidly. Therefore, we can expect the correlation to be weaker than -1.0, but still negative, with a value likely to be around -0.6, indicating a moderate degree of association between the two variables.

Question 4

All but one of the statements below contain a mistake. Which one could be true?
A) The correlation between a person's age and vision (20/20?) is r = -1.04.
B) The correlation between blood alcohol level and reaction time is r = 0.73.
C) There is a high correlation between cigarette smoking and gender.
D) The correlation between the species of tree and its height is r = 0.56.
E) The correlation between age and weight of a newborn baby is r = 0.83 ounces per day.

Accepted Answer

Correlation coefficients range from -1 to 1. A correlation of r = 0.73 suggests a strong positive relationship between two variables, which is plausible for the relationship between blood alcohol level and reaction time.

Question 5

Researchers studying growth patterns of children collect data on the heights of fathers and sons.
The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely to be...
A) near +0.7
B) near -1.0
C) exactly +1.0
D) somewhat greater than 1.0
E) near 0

Accepted Answer

Height is a heritable trait, meaning that it is determined in part by genetics. Studies have shown that there is a positive correlation between the heights of fathers and their sons, but this correlation is not perfect. Based on this, the correlation between the fathers' heights and the heights of their 16-year-old sons is most likely to be near +0.7, indicating a strong positive relationship, but not a perfect one.

Question 6

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

Accepted Answer

The correlation coefficient ranges from -1 to 1, and a coefficient of 1.09 is impossible. Therefore, statement C is incorrect. The remaining statements all contain believable correlation coefficients, but statement E is the only one that does not contain a mistake.

Question 7

A business owner notes that for every extra hour his store is open, his total sales increase by a fixed amount. His most useful predictive model is probably……
A) exponential
B) power
C) quadratic
D) logarithmic
E) linear

Accepted Answer

The relationship between the extra hours the store is open and total sales is a linear relationship. This means that as the number of hours increases, the total sales will increase at a constant rate. Therefore, a linear model is the most suitable for predicting the total sales based on the number of extra hours the store is open.

Question 8

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

Accepted Answer

All of these options are potential problems that may arise in regression analysis between two variables.

Question 9

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) leverage.
C) an outlier.
D) regression.
E) extrapolation.

Accepted Answer

This scenario describes a lurking variable, which is a variable that is not directly measured or considered, but still influences the relationship between the two observed variables.

Question 10

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 a good model.
E) 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 11

The auto insurance industry crashed some test vehicles into a cement barrier at speeds of 5 to 25 mph to investigate the amount of damage to the cars. They found a correlation of r = 0.60 between speed (MPH) and damage ($). If the speed at which a car hit the barrier is 1.5 standard deviations above the mean speed, we expect the damage to be_______ the mean damage.
A) 0.36 SD above
B) equal to
C) 0.90 SD above
D) 1.5 SD above
E) 0.60 SD above

Accepted Answer

The answer of The auto insurance industry crashed some test...

Question 12

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 cheerios = 0.56 + 5.11(diameter).

-The slope of this model is best interpreted in context as……
A) For every 5.11 inches of diameter, the circumference is about 1 cheerio bigger.
B) It takes 5.11 cheerios to fill a plate's circumference.
C) For every 1 inch of diameter, the circumference holds about 0.56 more cheerios.
D) A mistake, because n is about 3.14 and that should be the slope.
E) For every 1 inch of diameter, the circumference holds about 5.11 more cheerios.

Accepted Answer

The slope in a linear model represents the rate of change. In this context, the slope of 5.11 indicates that for every 1 inch increase in diameter, the number of cheerios that fit on the circumference increases by about 5.11.

Question 13

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

Accepted Answer

Since the farmer has increased his wheat production by about the same percentage each year, an exponential model would be the most useful predictive model as it reflects a constant growth rate over time.

Question 14

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

Accepted Answer

An influential data point is one that, when removed, significantly changes the slope of the regression equation. This means it has a substantial impact on the model's parameters, unlike points with small residuals or those that are merely extreme in one direction without influencing the model's fit.

Question 15

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) both will decrease.
B) both will remain the same.
C) both will increase.
D) b will decrease, and r will increase.
E) b will increase, and r will decrease.

Accepted Answer

The point in the upper right corner is an outlier and has a strong influence on the slope of the line of best fit. Therefore, removing this point will reduce the magnitude of the slope (b will decrease). Additionally, since the outlier was positively correlated with the rest of the data, removing it will decrease the correlation between the remaining data points (r will increase). Therefore, the correct answer is D.

Question 16

A consumer group collected information on HDTVs. They created a linear model to estimate the cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the slope of the line of best fit?
A) 7
B) 0.70
C) 700
D) 7000
E) 70

Accepted Answer

The slope of the line of best fit represents the change in the dependent variable (cost of HDTV) for a one-unit change in the independent variable (screen size). Since the cost of an HDTV typically increases as the screen size increases, the slope is likely to be positive. Among the given choices, only E (70) is a positive value that represents a reasonable change in cost for a one-inch increase in screen size.

Question 17

The residuals plot for a linear model is shown. Which is true? 
A) The linear model is no good because of the curve in the residuals.
B) The linear model is okay because approximately the same number of points are above the line as below it.
C) The linear model is no good because some residuals are large.
D) The linear model is no good because the correlation is near 0.
E) The linear model is okay because the association between the two variables is fairly strong.

Accepted Answer

The answer of The residuals plot for a linear model...

Question 18

R-sq is a measure of ……
A) the percentage of the accuracy of the regression equation.
B) the proportion of the variability in the response variable that is explained by the explanatory variable.
C) the initial predicted starting point of the response variable when x is zero.
D) the probability that the regression line makes a correct prediction.
E) the change in the y-variable that corresponds with the change in the x-variable.

Accepted Answer

R-sq (R-squared) is a statistical measure that represents the proportion of the variability in the response variable that is explained by the explanatory variable. It ranges from 0 to 1, with higher values indicating a better fit of the regression line to the observed data. Therefore, option B is the correct answer. Option A, C, D, and E are incorrect as they do not accurately represent what R-sq measures.

Question 19

The correlation between X and Y is r = 0.35. If we double each X value, decrease each Y by 0.20, and interchange the variables (put X on the Y-axis and vice versa), the new correlation
A) is 0.50
B) is 0.90
C) is 0.35
D) is 0.70
E) cannot be determined.

Accepted Answer

The correlation coefficient (r) is not affected by changing the scale or location of X or Y, nor by interchanging the variables. Thus, the correlation remains r = 0.35.

Question 20

When using midterm exam scores to predict a student's final grade in a class, the student would prefer to have a
A) residual equal to zero, because that means the student's final grade is exactly what we would predict with the model.
B) negative residual, because that means the student's final grade is lower than we would predict with the model.
C) negative residual, because that means the student's final grade is higher 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) positive residual, because that means the student's final grade is lower 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, which would be preferable for the student as it means they performed better than expected.

Quiz 2: Data

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

A correlation of zero between two quantitative variables means that

It takes a while for new factory workers to master a complex assembly process. During the first month new employees work, the company tracks the number of days they have been on the job and the length of time it takes them to complete an assembly. The correlation is most likely to be

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

Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely to be...

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

A business owner notes that for every extra hour his store is open, his total sales increase by a fixed amount. His most useful predictive model is probably……

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

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

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 cheerios = 0.56 + 5.11(diameter) . -The slope of this model is best interpreted in context as……

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

If a data point is influential it……

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 consumer group collected information on HDTVs. They created a linear model to estimate the cost of an HDTV (in $) based on the screen size (in inches) . Which is the most likely value of the slope of the line of best fit?

The residuals plot for a linear model is shown. Which is true?

R-sq is a measure of ……

The correlation between X and Y is r = 0.35. If we double each X value, decrease each Y by 0.20, and interchange the variables (put X on the Y-axis and vice versa) , the new correlation

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