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Chapter 12: Q. 72 (page 726)

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

a. Using 鈥渟tories鈥� as the independent variable and 鈥渉eight鈥� as the dependent variable, make a scatter plot of the data.

b. Does it appear from inspection that there is a relationship between the variables?

c. Calculate the least squares line. Put the equation in the form of: \(\hat{y}=a+bx\)

Short Answer

Expert verified

Part a. While creating scatter plot, consider 鈥渟tories 鈥渁s an independent variable on \(X\) axis and consider 鈥渉eight 鈥渁s a independent variable on \(Y\) axis. The scatter plot is made using the excel sheet.

Part b. From scatter plot we can say that there will be positive linear relationship between heights and stories.

Part c.

Step by step solution

01

Part a. Step 1. Explanation

While creating scatter plot, consider 鈥渟tories 鈥渁s an independent variable on \(X\) axis and consider 鈥渉eight 鈥渁s a independent variable on \(Y\) axis. The scatter plot is made using the excel sheet.

02

Part b. Step 1. Explanation

From scatter plot we can say that there will be positive linear relationship between heights and stories.

03

Part c. Step 1. Explanation

The general least square line is given by,

\(y=a+bx\).....(1)

Here, \(a\) is the \(y\) intercept and \(b\) is the slope.

Here \(y\) is the dependent variable and \(x\) is independent variable.

The least square line is calculated by using above excel sheet.

By using equation (1) the estimated least squares can be written as,

\(y=a+bx\).....(1)

height\(=102.43=11.758\)stories

\(y=102.43+11.758x\)....(2)

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Most popular questions from this chapter

58. Piece-rate systems are widely debated incentive payment plans. In a recent study of loan officer effectiveness, the following piece-rate system was examined:

%of goal reached
<80
80
100
120
Incentive
n/a
\(4,000with an additional \)125added per percentage point from 81-99%
\(6,500with an additional \)125added per percentage point from 101-119%
\(9,500with an additional \)125added per percentage point from 121%

If a loan officer makes 95%of his or her goal, write the linear function that applies based on the incentive plan table. In context, explain the

y-intercept and slope.

55. The Sum of Squared Errors for a data set of 18 numbers is 49.What is the standard deviation?

What would you predict the sales to be on day 60?

Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where xis the number of endorsements the player has and yis the amount of money made (in millions of dollars)

xyxy
02512
3849
2739
1303
5134
10

Whenn=100and r=-0.89, is there a significant correlation? Explain.

Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where xis the number of endorsements the player has and yis the amount of money made (in millions of dollars).

xyxy
02512
3849
2739
1303
513410

What is the slope of the line of best fit? What does it represent?

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