EXST 2201 Exam 3

If car prices followed the regression equation below, what would you expect the car price to be (on average) a year from now? (9.3.13) Car Price = 50,000 + (-100) × Months

$48,800.

Using the scatterplot below, match each point with its x,y coordinates. (9.2.2)

(3800, 32) -A (4900, 12) -B (5700, 44) -C (6300, 38) -D

What is the range of values for linear correlation measure? (9.1.14)

-1 to +1, inclusive ( [-1,+1] ).

How many of each variable below is there in simple linear regression? (9.3.3)

1- Predictor variable. Rational: 1- Response variable. Rational:

Why is a lurking variable important? (9.1.6)

Because it affects the statistical results without our knowledge.

In regression, given the descriptive statistics below for the variables Calories eaten (cal) and body Weight (grams) of white mice, what is the expected change in Weight for a 10 Calorie decrease in diet? (9.4.8)

Body Weight goes down 6 grams.

Which of the two scatterplots below show no relationship between two variables? (9.2.9)

Both scatterplots show no relationship.

In concept, how does linear regression find the regression line? (9.3.20)

By finding the line where the residuals of the points are the smallest.

How does the Rubber Band method indicate a high linear component? (9.2.22)

By forming a narrow oval shape.

Conceptually, how is the information about a linear relationship summarized in linear regression? (9.1.16)

By the line of best fit through the middle of the scatterplot.

Using the linear regression information below relating the batting average (Average) of a baseball team with the number of home runs scored in a season (Home_Runs), match each statement with its appropriate value. (9.4.12) A. Expected number of home runs with a batting average of 0.263 (use sample information). B. The appropriate value for the population slope (use population information). C. The change in home runs for a 0.01 batting average increase (use sample information).

A. Expected number of home runs with a batting average of 0.263 (use sample information). - 188.8 home runs. B. The appropriate value for the population slope (use population information). - 0.0 home runs/batting average unit. C. The change in home runs for a 0.01 batting average increase (use sample information). - Go down 2.31 home runs.

With binomial data, match each condition with its proper continuity corrected x-value. (10.1.11)

A. Probability greater than or equal to 11. - x=10.5 B. Probability less than or equal to 10. - x=10.5 C. Probability less than 11. - x=10.5 D. Probability greater than 10. - x=10.5

Using the linear regression information below relating the size of a female's brain (MRI Count) with her Intelligence Quotient (IQ) , match each statement with its appropriate value. (9.4.11) A. The appropriate value for the population slope (use population information). B. The change in IQ for a 100 MRI count increase (use sample information). C. Expected IQ of a female with a MRI count of 900 (use sample information).

A. The appropriate value for the population slope (use population information). - 0 IQ units/MRI count. B. The change in IQ for a 100 MRI count increase (use sample information). - Go up 1.7 IQ units. C. Expected IQ of a female with a MRI count of 900 (use sample information). - 134.7 IQ units.

Using the linear regression information below relating the size of a diamond (Carats) with its Price (dollars) , match each statement with its appropriate value. (9.4.10) A. The change in Price for a one Carat size increase (use sample information). B. The appropriate value for the population slope (use population information). C. Expected price for a four (4) carat diamond (use sample information).

A. The change in Price for a one Carat size increase (use sample information). - Go up 12,092 dollars. B. The appropriate value for the population slope (use population information). - 12,092 dollars/carat. C. Expected price for a four (4) carat diamond (use sample information). - 7,123 dollars.

In regression, given the descriptive statistics below for the variables Outside Temperature (degree F) and Air Conditioning Cost (dollars), what is the expected change in AC Cost for a 1-degree F increase in Outside Temp? (9.4.5)

AC cost goes up 12.7 dollars.

How does an extreme value affect the linear correlation coefficient? (9.2.24)

All of the other answers.

Select the two important points to remember when interpreting statistics of movement. (9.1.4)

Always look at the data first. Movement is not causation.

In regression, given the descriptive statistics below for the variables Calories eaten (cal) and body Weight (grams) of white mice, what is the expected Weight for a diet of 100 Calories? (9.4.9)

An expected body Weight of 50.4 grams. 49.6

What type of relationship between two variables can a scatterplot detect? (9.1.9)

Any type of relationship.

With binomial data, select all choices that are part of the assumptions for a binomial event. (10.1.2)

Each event has the same probability of success. The result is recorded as a 0 or a 1.

In the table used to calculate the linear correlation coefficient by hand, in the last column titled (Zx × Zy) , how many plus (+) and minus (-) signs would you expect for a correlation coefficient near zero (0). (9.2.17)

Equal number of (+'s) and (-'s).

In regression, given the descriptive statistics below for the variables Outside Temperature (degree F) and Air Conditioning Cost (dollars), what is the expected AC Cost for an 80-degree F Outside Temp? (9.4.6)

Expected AC cost is 1,022 dollars.

What is movement between two columns of data values? (9.1.7)

How the value of one variable moves in relation to the value of the other variable.

What does the statistical method of linear regression do? (9.3.2)

It finds the equation (slope and y-intercept) of the middle line.

What new information does linear regression give over linear correlation? (9.3.5)

It gives the magnitude (size) of the effect of the predictor variable on the response variable.

binomial data: How many tail(s) situation is a confidence interval for the population proportion? (10.2.9)

It is always a two-tail situation.

In regression, what do the terms Least Squares mean (9.4.2)

Least, means the smallest value for the sum. Squares, means all the residuals have been squared.

Select the two parts done when analyzing a scatterplot. (9.2.3)

Look at the overall pattern. Look for any exceptions to the overall pattern.

With binomial data, using the information below, what is the value of the mean and standard deviation to use to find probability? (10.1.10) n = 60 ; p = 0.45

Mean = 27 ; Standard deviation = 3.85 .

What calculation provides the foundation for the method of linear correlation? (9.2.16)

Multiplying two z-scores together.

With binomial data, can a normal curve be used to approximate the probability of all binomial experiments? (10.1.8)

No, as not all binomial histograms are unimodal and symmetrical enough for the normal curve to fit well.

binomial data: Shouldn't the binomial histogram be approximated by the t-curve, since the population standard deviation is not known? (10.2.8)

No, because it is an approximation and the z-curve is a better fit.

In regression, if a residual tells how close a single point is to a line, can the sum of all residuals be used to find the actual regression line. (9.4.1)

No, because the sum of all residuals always equals zero.

With binomial data, are histograms of binomial events interesting? (10.1.3)

No, because they contain only two bars.

With binomial data, do all the variables below contain binomial data? (10.1.1)

No, only the variable Vote contains 0's and 1's.

How many possible extreme values can be seen in the scatterplot below? (9.2.11)

One possible extreme value at coordinates (66, 200).

What type of relationship between two variables can linear correlation detect? (9.1.12)

Only a linear relationship.

What type of relationship does linear correlation measure? (9.2.15)

Only a linear relationship.

binomial data: What data values are appropriate to calculate the sample proportion? (10.2.4)

Only two data values (0 and 1).

Where does a lurking variable lurk? (9.1.5)

Outside of the data values collected.

Select the exceptions to the overall patterns looked for when analyzing a scatterplot. (9.2.10)

Pattern of any events. The presence of extreme values. More than one cluster (group).

Two scatterplots are plotted in the graph below, which scatterplot shows the higher linear correlation coefficient? (9.2.23)

Plot B, because its points are closer to a line.

Two separate scatterplots are shown below, though they have different directions of relationship, which scatterplot shows a higher linear relationship? (9.2.7)

Plot B, because its points are closer to a line.

Please match each variable with where it is plotted in a scatterplot. (9.1.10) - The response variable - The predictor variable

Plotted on the x-axis. - The predictor variable Plotted on the y-axis. - The response variable

Which of the points below would be closest to the regression line? (9.3.19) Point A: with residual = +150 Point B: with residual = -120 Point C: with residual = -10 Point D: with residual = +12

Point C, as it has the smallest magnitude of the residuals (-10).

With binomial data, the state police estimate that 35% of highway drivers speed over 80 mph. If 100 highway drivers are stopped, what is the probability that more than 50 of them were speeding over 80 mph? (np (1-p) = 22.75 ) (10.1.12)

Probability = 0.0006 .

With binomial data, a veterinarian estimates that 40% of people don't have their dogs vaccinated. If 100 people are selected , what is the probability that at least 50 of them don't have their dog vaccinated? (np (1-p) = 24) (10.1.14)

Probability = 0.0262 .

With binomial data, a dentist estimates that 65% of people don't floss enough. If 100 people are selected , what is the probability that 60 or more of them don't floss enough? (np (1-p) = 22.75 ) (10.1.13)

Probability = 0.8749 .

With binomial data, it is known that 80% of women wear lipstick of some type of red color. If 100 women are asked , what is the probability that no more than 90 of them wear lipstick of some type of red color? (np (1-p) = 16) (10.1.15)

Probability = 0.9956 .

What is NOT an appropriate comment because of the Scope of the Model? (9.3.15)

Regression is good for extrapolation outside of the range of the predictor variable.

Using the regression equation below, what would be the residual for a point with the coordinates (10,80)? (9.3.17) Weight = -12.3 + 9 × Height

Residual = +2.3 .

Using the regression equation below, what would be the residual for a point with the coordinates (24,45000)? (9.3.18) Car Price = 50,000 + (-100) × Months

Residual = -2,600 .

binomial data: How is the sample proportion calculated? (10.2.3)

Same as the sample average, add up the data values and divide by n.

binomial data: How is the standard error of the sample proportion calculated? (10.2.5)

Same as the standard error of the sample average, (standard deviation√n)

In regression, given the descriptive statistics below for two dependent variables, what is the value of the sample slope / the sample y-intercept of the regression line? (9.4.7)

Sample slope = 0.6 / sample y-intercept = -9.6 or -10.4.

In regression, given the descriptive statistics below for two dependent variables, what is the value of the sample slope / the sample y-intercept of the regression line? (9.4.4)

Sample slope = 12.7 / sample y-intercept = 6.0.

Match each use of linear regression below with the parts of the regression equation needed for that use. (9.3.14) A.- Prediction of the value of the response variable from the value of the predictor variable. B.- Explanation of the effect of the predictor variable on the response variable.

Slope of the regression equation (b(1)). - Explanation of the effect of the predictor variable on the response variable. y-Intercept and slope of the regression equation ((b(0),b(1)). - Prediction of the value of the response variable from the value of the predictor variable.

If scatterplots are so useful to see variable relationships, why is a statistical method using mathematics needed? (9.2.14)

Some scatterplots are so amorphous that it can be hard to see any pattern. A scatterplot does not quantify any relationship.

What two assumptions need to be met to do linear regression? (9.3.7)

That a linear relationship does exist for these two variables. That the data values are normally distributed (vertically) around the regression line.

What method is used to visually estimate the linear component in a scatterplot? (9.2.5)

The Rubber-Band method.

What two characteristics of linear relationship are expressed in a correlation coefficient? (9.2.18)

The direction of the linear relationship expressed in the mathematical sign. The strength of the linear relationship expressed in the magnitude of the value.

What statistical method will this book use to calculate the equation of the line in linear regression? (9.1.17)

The least-squares method of linear regression.

binomial data: What characteristic of a column of data does proportion measure? (10.2.2)

The location of the column of data values.

binomial data: Select the two components of a confidence interval for the population proportion? (10.2.10)

The location of the confidence interval. The margin of error of the confidence interval.

What information does linear regression give that linear correlation does not give? (9.1.15)

The magnitude of the effect of the linear relationship.

Using the regression equation below, how much would you expect Weight (lbs) to change on average if Height (ins) went up one inch? (9.3.8)

Weight would go up 9 lbs.

Are two columns of both the Height and Weight of individuals appropriate to measure movement? (9.1.3)

Yes, because both height and weight come from one individual.

Can linear correlation measure a linear relationship, as well as just detect it? (9.1.13)

Yes, it can measure both the direction and the strength of the linear relationship.

Is there an event shown in the scatterplot below? (9.2.12)

Yes, there appears to be an event of some kind from x=3 to x=9.

Select the values of a correlation coefficient that indicate a strong linear relationship. (9.2.20)

r = (-1) r = (+1)

Match each scatterplot with its correlation coefficient. (9.2.21)

r = -0.3 - A r = +0.5 - B r = +0.9 - C r = -0.99 - D

With binomial data, what is the difference between a binomial event and a binomial experiment? (10.1.4)

A binomial experiment is a set number of binomial events.

What type of variable relationship is shown in the scatterplot below? (9.2.8)

A curvi-linear relationship.

If a point gives the middle of a column of data values, what gives the middle of a scatterplot? (9.3.1)

A line going through the middle of the scatterplot.

Select the overall patterns looked for in analyzing a scatterplot. (9.2.4)

A linear relationship. A curvi-linear relationship. No relationship.

Assume that two separate scatterplots (A and B)are shown below, match each scatterplot with its direction of linear relationship. (9.2.6)

A negative relationship. - B A positive relationship. - A

Select all choices that are the statistical methods used to measure variable relationship. (9.1.8)

A scatterplot. Linear correlation. Linear regression.

Using the regression equation below, how much would you expect Weight (lbs) to change on average if Height (ins) went down ten inches? (9.3.9) Weight = -12.3 + 9 × Height

Weight would go down 90 lbs.

binomial data: A statistics instructor at a local college sampled 100 of her students and found that 25 of them actually liked statistics. What is the 95% confidence interval for the population proportion of students liking statistics? (10.2.11)

CI = (0.16, 0.33).

In the thought concept of variable relationship, please match each variable with when it changes. (9.1.11) - The predictor variable - The response variable

Changes before the response variable changes. - The predictor variable Changes after the predictor variable changes. - The response variable

With binomial data, using the information below, what is the value of the Condition to use the normal approximation? (10.1.9) n = 30 ; p = 0.15

Condition = 3.8.

In Chapter 09, what characteristic of columns of data values is being measured? (9.1.1)

The movement between two columns of data values.

With binomial data, if the critical parameters for a normal distribution are mean (μ) and standard deviation (σ), what are the critical parameters for a binomial distribution? (10.1.5)

The number of events in the experiment (n). The probability of success of each event (p).

With binomial data, if n is the symbol for the number of events, then what is x the symbol for? (10.1.6)

The number of successes in the experiment.

binomial data: Using confidence intervals, how could you tell if the means of two, or more, populations might be the same. (10.2.12)

The population means might be the same if the confidence intervals overlapped.

Below is the equation of a regression line, match each symbol with its meaning. (9.3.6) ŷ = b0 + b1x -The predicted value of the y-variable. -The y-intercept of the regression line. -The slope of the regression line. -The value of the x-variable.

The predicted value of the y-variable. - (ŷ) The y-intercept of the regression line. - (b0) The slope of the regression line. - (b1) The value of the x-variable. - (x)

binomial data: What does the statistical word proportion mean? (10.2.7)

The proportion of successes in a binomial experiment.

binomial data: What statistic for continuous data is analogous to the sample proportion? (10.2.1)

The sample average (x̄).

binomial data: What is the shape of the sample proportion? (10.2.6)

The shape of the normal curve, after the condition to use the normal approximation is met.

In regression, which of the following choices is true when the regression line is found? (9.4.3)

The sum of the squared residuals has the smallest value possible.

In concept, what is a regression residual? (9.3.16)

The vertical distance a data point (x,y) is from the regression line.

From a statistics standpoint, why are the values of the slope and y-intercept needed? (9.3.4)

They summarize the relationship information in the data set.

What are the two uses of linear regression? (9.3.11)

To explain the change in the response variable from a change of the predictor variable. To predict the value of the response variable from the value of the predictor variable.

With binomial data, what does the phrase Normal Approximation to the Binomial mean? (10.1.7)

To use the normal curve to approximate the probability of a binomial histogram.

What is a scatterplot used for in the field of statistics? (9.2.1)

To visually see the pattern of the relationship between two variables.

What is needed to measure the movement between two columns of data values? (9.1.2)

Two columns of dependent data values.

How many clusters are seen in the scatterplot below? (9.2.13)

Two definite clusters, perhaps three.

Match each linear relationship with the movement of the variable data values. (9.2.19)

Variable data values move in the same direction. - A positive linear relationship. Variable data values move in opposite directions. - A negative linear relationship. Variable data values move independently of each other. - No linear relationship.

If car prices followed the regression equation below, would you wait to buy a car or would you buy a car now? (9.3.12) Car Price = 50,000 + (-100) × Months

Wait to buy as car prices are on average dropping $100 per month.

Using the regression equation below, how much would you expect Weight (lbs) to change on average if Height (ins) went up two inches? (9.3.10) Weight = -12.3 + (-9) × Height

Weight would go down 18 lbs.