Chapter 3, Problem 7CRE

(a)

To determine

To find: The correlation increase, decrease or stay being the same.

Answer to Problem 7CRE

The correlation decreases.

Explanation of Solution

Given information:

The correlation for all 50 states in the figure is 0.408.

The change in the correlation if on removing Hawaii is explained as below,

Correlation analysis is used to measure the strength of the association between variables. In other words, it can be said that correlation describes the linear associations between quantitative variables.

Since, correlation is sensitive to outliers, the correlation will be affected due to the data point Hawaii.

The data point of Hawaii is higher end outlier and it is above average corresponding to both the variables Maximum 24-hour participation and Maximum annual participation.

Since, the outlier is at the higher end, the correlation decreases by removing the higher end data point.

Therefore, the correlation decreases.

Conclusion:

The correlation decreases.

(b)

To determine

To analyse: The line that predicts the two least square lines.

Answer to Problem 7CRE

The blue line is the least squares line with all 50 states and the red line is the least squares line without the data point Hawaii.

Explanation of Solution

Given information:

Two least-squares lines ate shown on the graph. One was calculated using all 50 states, and the other omits Hawaii.

Identify the least squares line with the data point Hawaii and without the data point Hawaii:

It is known that the correlation decreases by removing the data point.

Since, there is a proportional relationship between the correlation coefficient and regression coefficient, the regression coefficient also decreases by removing the data point Hawaii.

The least squares line with small slope is the line without the data point Hawaii.

The least squares line with small slope is the line with the data point Hawaii.

Therefore, the blue line is the least squares line with all 50 states and the red line is the least squares line without the data point Hawaii.

Conclusion:

The blue line is the least squares line with all 50 states and the red line is the least squares line without the data point Hawaii.

(c)

To determine

To analyse: The factor that will affect the correlation and the last-squares line

Answer to Problem 7CRE

The switching the explanatory and response variables, the least squares line will change.

Explanation of Solution

Given information:

The Following would affect the correlation, s, and the last-squares line:

• Measuring record precipitation in feet instead of inches for both variables
• Switching the explanatory and response variables

The correlation will affect  s  and the least squares line:

Measuring record precipitation in feet instead of inches for both variables:

• By changing the units the correlation will not change.
• The standard error s will decrease by changing the units.
• By changing the units, the slope of the least squares line will not change as the units of both the dependent and independent variables are changed but the intercept value will change.

Switching the explanatory and response variables:

• By switching the explanatory and response variables, the correlation will not change.
• The standard error s will decrease by switching the explanatory and response variables.
• By switching the explanatory and response variables, the least squares line will change.

Conclusion:

The switching the explanatory and response variables, the least squares line will change.