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### Analysis of LSRL

EQ: How well does the line fit the data?

What would you conclude based on the graph?

Data from 1860-1940

Barrels of Rum Sold

Ministers in Boston

Reasons for strong correlation

- Lurking variables: Something in the background that affects both variables the same way.

For the historical data, as population increased the number of ministers increased as did the amount of alcohol being sold.

Shoe size vs. Height

Determine if a linear model is a good idea.

Create a scatterplot and examine the relationship.

DON’T FIND THE LSRL!!!!

Interpret all of the values

r : There is a strong positive linear relationship

a: when the shoe size is 0 the height

will be 51.36 inches

b: for every 1 increase in shoe size

the height will increase by 1.87 inches

Coefficient of Determination

The percent of variation in the y values that is explained by the linear model with x.

Coefficient of determination = r2

where r is the correlation.

The coefficient of determination between shoe size and height is .8575.

What does this mean????

85.75% of the variation in heights is explained by the linear model with shoe size.

Residuals height is .8575.

A residual is the

difference

between an

observed

value of the response variable and the value

predicted

by the

LSRL

Predictions height is .8575.

Predict the height of a person with a shoe size of 8.5

Residual height is .8575.

Actual Data:

Residual:

Observed - Predicted

8.5 shoe size and 66 inches for height

66-67.25 =-1.25

Create the LSRL height is .8575.

Calculate Residuals height is .8575.

Evaluate Residual Plot height is .8575.

A good residual plot has

No patterns

No outliers

Balance between +’s and –’s

Bad Residual Plots height is .8575.

Example height is .8575.

How are American female (30-39) heights and weights related?

- Create a scatterplot and comment on the relationship
- Determine the LSRL, r, and r2 and interpret the values.
- Evaluate the model by analyzing the residuals.
- Predict the weight for a 63 inch female.
- Calculate the residual for a 63 inch female.
- How confident are you in your prediction?

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