Chapter 4: Q. 4.125 (page 189)
If tends to increase linearly as increases, the variables are------ linearly correlated.
Short Answer
Positively
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Chapter 4: Q. 4.125 (page 189)
If tends to increase linearly as increases, the variables are------ linearly correlated.
Positively
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To determine whether is positive, negative, or zero.

U.S. Presidents. The data from Exercise 4.71 for the ages at the inauguration and of death for the presidents of the United States are on the Weissstats site.
a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also do parts (b) and (c).
b. obtain the linear correlation coefficient.
c. interpret the value of in terms of the linear relationship between the two variables in question.
Tine Series. A collection of observations of a variable y taken at regular intervals over time is called a time series. Bocoomsic data and electrical signals are examples of time series. We can think of a time series as providing data points where is the ith observation time and is the observed value of y at time . If a time series exhibits a linear trend, we can find that trend by determining the regression equation for the data points. We can then use the regression equation for forecasting purposes.
As an illustration, consider the data on the WeissStats site that shows the U.S. population, in millions of persons, for the years 1900 2013. as provided by the I.S. Census Beret.
a. Use the technology of your choice to lesbian a scatterplot of the data.
h. Use the technology of your choice to find the regression equation.
6. Use your result from part (b) to forecast the U.S. population for the years 2014 and 2015 .
In Exercise 4.5, we give linear equations. For each equation,
a. find the -intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
Given equation is,
The linear correlation coefficient of a set of data points is .
a. Is the slope of the regression line positive or negative? Explain your answers.
b. Determine the coefficient of determination.
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