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Question 1

Linear regression model

Answer 1

uses an explanatory variable to predict the response variable

Question 2

Explanatory variable

Answer 2

x

Question 3

Response variable

Answer 3

y

Question 4

Predicted response variable

Answer 4

y with hat on top

Question 5

Predicted response variable equation

Answer 5

y^ = a + bx

Question 6

Constant

Answer 6

a

Question 7

Slope

Answer 7

b

Question 8

Extrapolation

Answer 8

occurs when a linear model is used to predict a response value for explanatory variable that is beyond the interval of x-values to determine the regression line

Question 9

Least-Squares Regression Line

Answer 9

Line of best fit
Sum of squared residuals as small as possible
Helps predict the other value

Question 10

Slope (b)

Answer 10

the amount by which y is predicted to change when x increases by 1

Question 11

There is one point all regressions pass through and that is

Answer 11

(x^-,y^-) mean

Question 12

When L1 & L2 are filled out, how can you calculate LSRL equation

Answer 12

stat -> calc -> 8

Question 13

Identify the slope of the regression line found in example and explain what it means in context

Answer 13

A (x context) increases by 1 unit, the predicted (y context) increases by (b)

Question 14

Identify the y intercept of the regression line found in example and explain what it means in context

Answer 14

When the (x context) is 0, the predicted (y context) is (a) (y units)

Question 15

Slope of regression line formula

Answer 15

b = r(Sy/Sx)

Question 16

r^2

Answer 16

coefficient of determination. The proportion of variation in the response variable that is EXPLAINED by the explanatory variable

Question 17

What are the coefficients of the least squares regression model

Answer 17

y intercept (a) and estimated slope (b)

Question 18

y intercept formula

Answer 18

a = y^- - b^-

Question 19

Standard deviation of residuals

Answer 19

gives the typical error

Question 20

r^2 formula

Answer 20

r^2 = 1 - (E(y - y^)^2/E(y-y^-)^2

Question 21

r^2 is expressed as

Answer 21

a percentage and does not have units

Question 22

r^2 and S both tell us how well the linear model fits our data so

Answer 22

always make note of both when analyzing data

Question 23

The standard deviation of the residuals is measured in

Answer 23

the units of the response variable

Question 24

Interpret the coefficient of determination

Answer 24

(r^2)% of the variation in (y context) is explained by (x context).

Question 25

Interpret the SD of the residuals

Answer 25

The typical error in (y context) based on (x context) is (S) (response units)

Question 26

Constant

Answer 26

a = y int

Question 27

Influential observation

Answer 27

A point that if removed will change relationship (r) dramatically

Question 28

High leverage point

Answer 28

A point that has a substantially larger or smaller x value compared to the other ovservations

Question 29

An influential point may have a small residual but

Answer 29

still have a great effect on the regression line

Question 30

Most extreme x values will not necessarily have the largest residuals but

Answer 30

usually have the most impact on the regression line and correlation

Question 31

Extreme values in the x or y direction usually affect the slope in a similar way but

Answer 31

x direction outliers tend to change the correlation more drastically

Question 32

Residual

Answer 32

left over vertical variation in the response variable (y) from the LSRL
Every observation will have a residual

Question 33

Residual plot

Answer 33

Scatter plot of residuals plotted against explanatory variable. Used to determine if a linear model is appropriate for certain data sets

Question 34

Residual formula

Answer 34

= y - y^