Unit 2 - Linear Regression

Question 1

What is y hat?

Answer 1

Predicted y value

Question 2

What is the formula for the slope of a regression line?

Answer 2

a = r(sy/sx)

Question 3

What is an influential point?

Answer 3

A point, when removed, significantly changes the regression equation.

Question 4

Given a scatterplot, how can you tell if a linear model is appropriate?

Answer 4

The scatterplot shows a linear pattern.

Question 5

Given a residual plot, how can you tell if a linear model is appropriate?

Answer 5

The residual plot shows no pattern.

Question 6

Where can you find residuals on your calculator?

Answer 6

2nd STAT (List), 7: RESID

Question 7

Correlation will always be a number between ___ and ____.

Answer 7

1 and -1

Question 8

What does LSRL stand for?

Answer 8

Least Squares Regression Line

Question 9

What are the characteristics of a least squares regression line?

Answer 9

1. It contains the point (x-bar, y-bar)
2. The sum of the residuals is zero.
3. The sum of the squares of the residuals is the least number possible.

Question 10

Which correlation is stronger? .4 or - .5

Answer 10

-.5

Question 11

What is the formula for the least squares regression line?

Answer 11

y-hat = b + ax

Question 12

What is a residual?

Answer 12

The distance between a point and the regression line.

Question 13

What is the formula for a residual?

Answer 13

e = y-hat - y

Question 14

What is extrapolation?

Answer 14

Using a regression model to make a prediction outside the range of data collected.

Question 15

What is interpolation?

Answer 15

Using a regression model to make a prediction within the range of data collected.

Question 16

Given this equation, interpret the slope.

Globs-hat = 20 + 1.5 blags

Answer 16

For every increase in 1 blag, the number of globs increases by approximately 1.5.

Question 17

Given this equation, interpret the y-intercept.

Globs-hat = 20 + 1.5 blags

Answer 17

When there are zero blags, the number of globs is predicted to be 20.

Question 18

Explanatory Variable = calories
Response Variable = weight
R-sq = 82.3%
Interpret R-sq

Answer 18

82.3% of the variation in weight can be explained by the number of calories eaten.

Question 19

Describe a scatterplot with a correlation coefficient of r = -.5.

Answer 19

There is a moderate, negative, linear association between x and y.

Question 20

What is the formula for a residual?

Answer 20

e = y - yhat