exst final pt 4 (9.2-10.3)

binomial data: What is the difference between a descriptive 2x2 table of counts, and a contingency table?

A contingency table shows the expected frequencies in each cell.

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

A curvi-linear relationship.

binomial data: What is a chi-square test of independence?

A hypothesis test for two columns of binomial data.

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

A line going through the middle of the scatterplot.

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?

AC cost goes up 12.7 dollars.

Slope of the regression equation (b(1)).

Explanation of the effect of the predictor variable on the response variable.

binomial data: Select all parts of the Step A: Abstract for a chi-square test of independence?

Collect the counts of the data values of the two variables./Arrange in a 2x2 table and calculate the table totals.

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?

Expected AC cost is 1,022 dollars.

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?

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

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?

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

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

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

binomial data: In Step 2: Analyze for a chi-square test of independence, what are the expected frequencies?

The theoretical count in each cell if the variables are independent.

In concept, what is a regression residual?

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

binomial data: In a chi-square test of independence, using the information shown below, are these two variables independent? 10.3.11

These variables are dependent, because p-value = 0.005.

binomial data: In a chi-square test of independence, using the information shown below, are these two variables independent?

These variables are independent, because p-value = 0.3155.

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

They summarize the relationship information in the data set.

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

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

How many clusters are seen in the scatterplot below?

Two definite clusters, perhaps three.

binomial data: In Step A: Abstract for a chi-square test of independence, what are the final steps to complete the 2x2 table of descriptive statistics?

calculate the row totals/calculate the column totals

binomial data: In Step 1: Theorize for a chi-square test of independence, what are the shapes of the chi-square distributions?

curve is uni-modal/skewed to right

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

direction expressed in mathematical sign, strength of relationship expressed in magnitude

What are the two uses of linear regression?

explain change in response variable from change in predictor/predict value of response variable from value of predictor

In regression, what do the terms Least Squares mean

least, smallest value for sum/squares, all residuals have been squared

assumptions for linear regression

linear relationship exists, data values normally distributed around regression line

patterns looked for in analyzing a scatterplot

linear relationship, curvi-linear relationship, no relationship

the two parts done when analyzing a scatterplot.

look at the pattern, and any exceptions

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

patterns, extreme values, multiple clusters

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

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

Match each scatterplot with its correlation coefficient. B

r = +0.5

Match each scatterplot with its correlation coefficient. C

r = +0.9

Match each scatterplot with its correlation coefficient. A

r = -0.3

Match each scatterplot with its correlation coefficient. D

r = -0.99

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

$48,800.

binomial data: In Step 1: Theorize for a chi-square test of independence, how many tail(s) situation is this?

(100%) One-tail to the right situation.

How does an extreme value affect the linear correlation coefficient?

All of the other answers.

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?

An expected body Weight of 50.4 grams.

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

Residual = -2,600 .

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?

Body Weight goes down 6 grams.

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

Both scatterplots show no relationship.

In concept, how does linear regression find the regression line?

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

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

By forming a narrow oval shape.

binomial data: Select all parts of the Step 2: Analyze for a chi-square test of independence?

Calculate each cell's expected frequency./Calculate the value of the chi-square test statistic.

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).

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

binomial data: In Step A: Abstract for a chi-square test of independence, what are the hypotheses? (1)

H(0): Variables are independent.

binomial data: In Step A: Abstract for a chi-square test of independence, what are the hypotheses? (2)

H(1): Variables are dependent.

What does the statistical method of linear regression do?

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

What new information does linear regression give over linear correlation?

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

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

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

Which of the points below would be closest to the regression line? 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).

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

Residual = +2.3 .

What calculation provides the foundation for the method of linear correlation?

Multiplying two z-scores together.

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.

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

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

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

What type of relationship does linear correlation measure?

Only a linear relationship.

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

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

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.

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

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

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

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

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

The Rubber-Band method.

binomial data: In a chi-square test of independence, what is the p-value?

The area in one tail of the chi-square curve from the test statistic to infinity.

a negative linear relation

Variable data values move in opposite directions.

positive linear relationship

Variable data values move in the same direction.

no linear relationship

Variable data values move independently of each other.

If car prices followed the regression equation below, would you wait to buy a car or would you buy a car now? 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? Weight = -12.3 + (-9) × Height

Weight would go down 18 lbs.

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

Weight would go down 90 lbs.

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

Weight would go up 9 lbs.

binomial data: In a chi-square test of independence, using the information shown below, is being overweight related to eating fast food?

Yes, being overweight and eating fast food are related, because p-value = 0.0323.

Is there an event shown in the scatterplot below?

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