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Chapter 4: Q. 4.111 (page 182)

More Money, More Beer? The data for per capita income and per capita beer consumption for the 50states and Washington, D.C. from Exercise 4.77are on the Weiss Stats site.

(a) Decide whether finding a regression line for the data is reasonable. If so, then also do parts(b)-(d).

Short Answer

Expert verified

The regression line for the data is not-reasonable.

Step by step solution

01

Given Information 

Whether it is reasonable to find the regression line or not.

02

Explanation 

The scatterplot for the given data can be drawn by using the MINITAB:

Step 1: Choose Graph> Scatterplot

Step 2: Choose With Connect Line, and then click OK.

Step 3: UnderYvariables, enter a column of BEER

Step 4: UnderXvariables, enter a column of INCOME

Step 5: Click OK

03

Explanation 

The scatterplot obtained will be,

From the above scatterplot, it is not reasonable to find a regression line for the data because the observations are not scattered around a line. Hence, there is no linear pattern visible in the given data. Therefore, the parts (b) - (d) will be omitted.

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Most popular questions from this chapter

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 x1+y2where x0is the ith observation time and yiis the observed value of y at time xi. 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 .

Tax Efficiency. In Exercise 4.58, you determined a regression equation that relates the variables percentage of investments in energy securities and tax efficiency for mutual fund portfolios.

a. Should that regression equation be used to predict the tax efficiency of a mutual fund portfolio with 6.4%of its investments in energy securities? with 15%of its investments in energy securities? Explain your answers.

b. For which percentages of investments in energy securities is use of the regression equation to predict tax efficiency reasonable?

Answer true or false to each statement, and explain your answers.

a. The graph of a linear equation slopes upward unless the slope is 0 .

b. The value of the y-intercept has no effect on the direction that the graph of a linear equation slopes.

What can you say aboutSSE, SSR and the utility of the regression equation for making predictions if

a. r2=1?

b.r2=0?

Age and Price of Orions. In Table 4.2, we provided data on age and price for a sample of 11Orions between 2and 7years old. On the Weiss Stats site, we have given the ages and prices for a sample of 31Orions between 1and 11years old.

a. Obtain a scatterplot for the data.

b. Is it reasonable to find a regression line for the data? Explain your answer.
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