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# Regression to relate variables

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A bank has offices in six different markets. It is feasible to say the annual sales of offices are related to the population of the communities they are in. The dependent variable, y, is annual sales. The independent variable, x is market population. The data are as follows:

Data on Annual Sale and Market Population for Six Offices

Office y=Annual Sales (000s omitted) x=Market Population (000s omitted)
Ionia 500 20
Belding 325 8
Hastings 350 10
Lowell 400 16
Sunfield 250 5
Woodland 125 4

More data attached.

#### Solution Preview

Looking at the scatterplot, you can see the different plotted variables are close to the regression line. Only a couple are farther away, but not enough to skew the data. This would indicate the relationship is close. If you then look at the Pearson R (on the Excel chart) you see it is .93. This number too indicates a positive relationship, and a very strong one at that.

Suppose you have a number line with -1 at one end and ...

#### Solution Summary

A discussion and example explained for use of regression, scatterplot, and number line in relating variables.

\$2.19

## Regression Line Relating the Percentage to Number of Variables

See attached file.

Regression example

Number Percentage of variable x Number of variable y
1 3.6 1700
2 2.0 3078
3 0.3 1820
4 0.3 2706
5 0.2 2086
6 3.0 2299
7 0.0 676
8 1.0 2088
9 2.2 2013

1.1 Fit a regression line relating the percentage of variables X to the number of variables Y.
1.2 Test for the statistical significance of this regression line using the F test.
1.3 What is R2 for the regression line in Question 1.1?
1.4 What does R2 mean in Question 1.3?
1.5 What is s2y.x ?
1.6 Test for the statistical significance of the regression line using the T test.
1.7 What are the standard errors of the slope and intercept for the regression line in 1.1?

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