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Chapter 12: Q.1.2 (page 777)

Give the equation of the least-squares regression line. Define any variables you use.

Short Answer

Expert verified

The equation of the least-squares regression line is y^=-1.19311+0.0287280x.

Step by step solution

01

Given Information

02

Explanation

In the question that variable xbe the number of the years since 1700and the variable y be the U.S. population in the years 1790to 1880. Thus, the general equation will be as:

y^=a+bx

And the slope and the constant of the regression line is give in the previous question as:

a=-1.19311

b=0.0287280

Thus, the regression line is as:

y^=a+bx

鈬�y^=-1.19311+0.0287280x

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Most popular questions from this chapter

An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole and the player鈥檚 total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

A 95%confidence interval for the slope Bof the population regression line is

(a)7,897,179卤3,023,782

(b)7,897,179卤6,047,564

(c)鈭�4,139,198卤1,698,371

(d)鈭�4,139,198卤3,328,807

(e)鈭�4,139,198卤3,396,742

For the study of Jordanian children in Exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

(a) Calculate the test statistic.

(b) Find the P-value using Table B. Then obtain a more precise P-value from your calculator.

The swinging pendulum Mrs. Hanrahan鈥檚 precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable. Describe what you see. (b) The theoretical relationship between a pendulum鈥檚 length and its period is

period=2蟺glength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

Which of the following would provide evidence that a power law model of the form y=axbwhere b鈮�0andb鈮�1, describes the relationship between a response variable yand an explanatory variable x.

(a) A scatterplot of yversus xlooks approximately linear.

(b) A scatterplot of ln yversus xlooks approximately linear.

(c) A scatterplot of yversus ln xlooks approximately linear.

(d) A scatterplot of ln yversus ln xlooks approximately linear.

(e) None of these.

Which of the following is a categorical variable?

(a) The weight of automobiles

(b) The time required to complete the Olympic marathon

(c) The average gas mileage of a hybrid car

(d) The brand of shampoo purchased by shoppers in a

grocery store

(e) The average closing price of a particular stock on the

New York Stock Exchange
See all solutions

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