Chapter 2



AP Statistics- Chapter 8 Line of Best Fit

Errors = residuals =

Linear Regression Line:

• Describes how…

• Used to …

Most accurate Regression line:

• Called:

• Definition: minimizes…

• Form:

• Pieces:

b1 =

b0 =

• always …

• not

• on calculator:

Complete example on p. 187 in book (TI TIPS).

Interpreting the slope of the LSR line:

Interpreting the y-intercept:

Example:

A real estate agent studied the relationship between house prices and size (square footage). He found the least-squares regression line to be: Selling Price = 51912.73 + 47.734(Square Feet).

a) Interpret the slope.

b) Interpret the Y-Intercept.

Extrapolation-

Coefficient of Determination-

• symbol:

• sentence interpretation:

RESIDUALS

Residuals (errors):

[pic] [pic]

Residual Plot:

Definition:

EXAMPLES:

Original plot residual plot

• Helps…

• No pattern = scattered =

• Pattern =

• On calculator:

GOOD: BAD: BAD:

Examples: TUITION (lists YR vs. TUIT); CAR (lists CMPG vs. CWT)

Assessing the fit of the linear model:

IS THE LINEAR MODEL A GOOD FIT FOR THE DATA?

COMPLETE WORKSHEETS 8B & 8C

Chapter 8: Linear Regression Computer Outputs

An insurance company conducts a survey of 15 of its life insurance agents. The average number of minutes spent with each potential customer and the number of policies sold in a week are noted for each agent.

The following is a printout from the statistical analysis tool on Microsoft Excel.

[pic]

1. What is the equation of the LSR line relating minutes spent and policies sold.

2. What is the value of r? What is the value of r2?

3. Interpret the slope in the context of the problem

The following is a MINITAB regression printout relating average number of degree-days per month to gas consumption (in cubic feet).

Predictor Coef StDev T P

Constant 123.24 28.60 4.31 0.004

Degree-d 20.221 1.145 17.66 0.000

S= 43.45 R-sq = 97.8% R-sq(adj) = 97.5%

1. What is the equation of the LSR line relating degree days to gas consumption?

2. What is the value of r? What is the value of r2?

3. Interpret the slope in the context of the problem.

Example 3:

[pic]

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