Question

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 “stories” as the independent variable and “height” 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

Part a. While creating scatter plot, consider “stories “as an independent variable on \(X\) axis and consider “height “as 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

Part a. Step 1. Explanation

While creating scatter plot, consider “stories “as an independent variable on \(X\) axis and consider “height “as a independent variable on \(Y\) axis. The scatter plot is made using the excel sheet.

Part b. Step 1. Explanation

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

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)