Question 1

When performing regression analysis, how can you evaluate how useful the regression equation is for making predictions?

Accepted Answer

The answer of When performing regression analysis, how can you...

Question 2

Describe what scatterplots are, and discuss their importance.

Accepted Answer

The answer of Describe what scatterplots are, and discuss their...

Question 3

A set of data consists of the number of years that applicants for foreign service jobs have studied German and the grades that they receive on a proficiency test. The following regression equation is obtained: $\hat { \mathrm { y } } = 31.6 + 10.9 \mathrm { x }$, where $\mathrm { x }$ represents the number of years of study and $\mathrm { y }$ represents the grade on the test. Identify the predictor and response variables.

Accepted Answer

The answer of A set of data consists of the...

Question 4

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal.
-The equation of the line is y = -5.6 - 6x.

Accepted Answer

A) Slopes downward 
B) Is horizontal 
C) Slopes upward

Question 5

Obtain the linear correlation coefficient for the data. Round your answer to three decimal places.
-$\begin{array}{r|rrrrr}
\mathrm{x} & 31.4 & 14.8 & 21.5 & 18.3 & 49.0 \
\hline \mathrm{y} & 10 & 7 & 4 & 6 & 6
\end{array}$

Accepted Answer

A) $- 0.121$ 
B)  $0.136$ 
C)  0 
D)  $- 0.136$

Question 6

In the context of regression analysis, if the regression sum of squares is large relative
to the error sum of squares, then the regression equation is useful for making predictions.

Accepted Answer

A) True 
 B)False

Question 7

A regression equation is obtained for a set of data. After examining a scatterplot, the researcher notices a data point that is potentially an influential observation. How could the researcher confirm that this data point is indeed an influential observation? How should the researcher proceed if the data point is found to be an influential observation?

Accepted Answer

The answer of A regression equation is obtained for a...

Question 8

Define the terms "predictor variable" and "response variable." Give an example of each.

Accepted Answer

The answer of Define the terms "predictor variable" and "response...

Question 9

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal.
-The equation of the line is $y = 14 + 6 x$.

Accepted Answer

A) Is horizontal 
B)  Slopes downward 
C)  Slopes upward

Question 10

Determine which scatterplot shows the strongest linear correlation.

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

The variables height and weight could reasonably be expected to have a positive linear correlation coefficient, since taller people tend to be heavier, on average, than shorter people. Give an example of a pair of variables which you would expect to have a negative linear correlation coefficient and explain why. Then give an example of a pair of variables whose linear correlation coefficient is likely to be close to zero.

Accepted Answer

The answer of The variables height and weight could reasonably...

Question 12

Create a scatterplot that shows a perfect positive linear correlation between x and y. How would the scatterplot change if the correlation showed each of the following? (a)a strong positive linear correlation; (b)a weak positive linear correlation; (c)no linear correlation.

Accepted Answer

The answer of Create a scatterplot that shows a perfect...

Question 13

For a compact car, a car-rental company charges $28.50 per day plus $0.15 per mile. For a one-day rental, let x denote the number of miles driven and let y denote the total cost. Obtain the equation that expresses y in terms of x. Construct a table of values using the x-values 70, 140, and 220 miles. Draw the graph of the equation by plotting the points from the table and connecting them with a straight line. Use the graph to estimate visually the cost of driving the car 190 miles.

Accepted Answer

The answer of For a compact car, a car-rental company...

Question 14

For a certain linear equation, as x increases from 3 to 4, the y-value increases from 17 to 22. The y-value corresponding to an x-value of 9 is 47. What is the y-value corresponding to an x-value of 10? Explain how you solved this problem.

Accepted Answer

The answer of For a certain linear equation, as x...

Question 15

For the linear equation $y = 6 + 4 x$, explain what the $y$-intercept and slope represent in terms of the graph of the equation.

Accepted Answer

A) The $\mathrm { y }$-intercept, $\mathrm { b } _ { 0 } = 6$, gives the $\mathrm { y }$-value at which the straight line $\mathrm { y } = 6 + 4 \mathrm { x }$ intersects the $x$-axis. The slope, $b _ { 1 } = 4$, indicates that the $x$-value increases by 4 units for every increase in $y$ of 1 unit. 
B)  The $y$-intercept, $b _ { 0 } = 4$, gives the $y$-value at which the straight line $y = 6 + 4 x$ intersects the $y$-axis. The slope, $b _ { 1 } = 6$, indicates that the $y$-value increases by 6 units for every increase in $x$ of 1 unit. 
C)  The $y$-intercept, $b _ { 0 } = 6$, gives the $y$-value at which the straight line $y = 6 + 4 x$ intersects the $y$-axis. The slope, $b _ { 1 } = 4$, indicates that the $x$-value increases by 4 units for every increase in $y$ of 1 unit. 
D)  The $y$-intercept, $\mathrm { b } _ { 0 } = 6$, gives the $\mathrm { y }$-value at which the straight line $\mathrm { y } = 6 + 4 \mathrm { x }$ intersects the $y$-axis. The slope, $b _ { 1 } = 4$, indicates that the $y$-value increases by 4 units for every increase in $x$ of 1 unit.

Exam 14: Descriptive Methods in Regression and Correlation

When performing regression analysis, how can you evaluate how useful the regression equation is for making predictions?

Describe what scatterplots are, and discuss their importance.

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal. -The equation of the line is y = -5.6 - 6x.

Obtain the linear correlation coefficient for the data. Round your answer to three decimal places. - $\begin{array}{r|rrrrr}\mathrm{x} & 31.4 & 14.8 & 21.5 & 18.3 & 49.0 \\\hline \mathrm{y} & 10 & 7 & 4 & 6 & 6\end{array}$

In the context of regression analysis, if the regression sum of squares is large relative to the error sum of squares, then the regression equation is useful for making predictions.

Define the terms "predictor variable" and "response variable." Give an example of each.

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal. -The equation of the line is $y = 14 + 6 x$ .

Determine which scatterplot shows the strongest linear correlation.

Create a scatterplot that shows a perfect positive linear correlation between x and y. How would the scatterplot change if the correlation showed each of the following? (a)a strong positive linear correlation; (b)a weak positive linear correlation; (c)no linear correlation.

For a certain linear equation, as x increases from 3 to 4, the y-value increases from 17 to 22. The y-value corresponding to an x-value of 9 is 47. What is the y-value corresponding to an x-value of 10? Explain how you solved this problem.

For the linear equation $y = 6 + 4 x$ , explain what the $y$ -intercept and slope represent in terms of the graph of the equation.

Exam 14: Descriptive Methods in Regression and Correlation

When performing regression analysis, how can you evaluate how useful the regression equation is for making predictions?

Describe what scatterplots are, and discuss their importance.

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal. -The equation of the line is y = -5.6 - 6x.

Obtain the linear correlation coefficient for the data. Round your answer to three decimal places. - x31.414.821.518.349.0y107466\begin{array}{r|rrrrr}\mathrm{x} & 31.4 & 14.8 & 21.5 & 18.3 & 49.0 \\\hline \mathrm{y} & 10 & 7 & 4 & 6 & 6\end{array}xy​31.410​14.87​21.54​18.36​49.06​​

In the context of regression analysis, if the regression sum of squares is large relative to the error sum of squares, then the regression equation is useful for making predictions.

Define the terms "predictor variable" and "response variable." Give an example of each.

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal. -The equation of the line is y=14+6xy = 14 + 6 xy=14+6x .

Determine which scatterplot shows the strongest linear correlation.

Create a scatterplot that shows a perfect positive linear correlation between x and y. How would the scatterplot change if the correlation showed each of the following? (a)a strong positive linear correlation; (b)a weak positive linear correlation; (c)no linear correlation.

For a certain linear equation, as x increases from 3 to 4, the y-value increases from 17 to 22. The y-value corresponding to an x-value of 9 is 47. What is the y-value corresponding to an x-value of 10? Explain how you solved this problem.

For the linear equation y=6+4xy = 6 + 4 xy=6+4x , explain what the yyy -intercept and slope represent in terms of the graph of the equation.

Obtain the linear correlation coefficient for the data. Round your answer to three decimal places. - $\begin{array}{r|rrrrr}\mathrm{x} & 31.4 & 14.8 & 21.5 & 18.3 & 49.0 \\\hline \mathrm{y} & 10 & 7 & 4 & 6 & 6\end{array}$

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal. -The equation of the line is $y = 14 + 6 x$ .

For the linear equation $y = 6 + 4 x$ , explain what the $y$ -intercept and slope represent in terms of the graph of the equation.