Analysis of lsrl
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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.

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Analysis of LSRL

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Analysis of lsrl

Analysis of LSRL

EQ: How well does the line fit the data?


What would you conclude based on the graph

What would you conclude based on the graph?

Data from 1860-1940

Barrels of Rum Sold

Ministers in Boston


Reasons for strong correlation

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

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!!!!


Find the lsrl using summary statistics

Find the LSRL using summary statistics


Interpret all of the values

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

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.


Analysis of lsrl

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

Residuals

A residual is the

difference

between an

observed

value of the response variable and the value

predicted

by the

LSRL


Predictions

Predictions

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


Residual

Residual

Actual Data:

Residual:

Observed - Predicted

8.5 shoe size and 66 inches for height

66-67.25 =-1.25


Create the lsrl

Create the LSRL


Calculate residuals

Calculate Residuals


Evaluate residual plot

Evaluate Residual Plot

A good residual plot has

No patterns

No outliers

Balance between +’s and –’s


Bad residual plots

Bad Residual Plots


Example

Example

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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