Chapter 1.10, Problem 17E

(a)

To determine

The sketch a scatter plot of the data. Let $y$ represent the length of the winning discus throw (in feet) and let $t=20$ represent $1920$ .

Answer to Problem 17E

The value of the angle $\cos \theta =\frac{\sqrt{2}}{2}$ in degrees and in radians are $45°$ and $\frac{\pi }{4}\text{rad}$ .

Explanation of Solution

Given information:

The length (in feet) of the winning men’s discus throws in Olympics from $1920$ through $2008$ is shown in table.

  

Calculation:

Scatter plot of data is shown below figure.

  

Therefore, the sketch of a scatter plot is shown in figure.

(b)

To determine

The equation of the line using straightedge to sketch the best-fitting line through the points.

Answer to Problem 17E

The equation of the line $y\approx t+130$ .

Explanation of Solution

Given information:

The length (in feet) of the winning men’s discus throws in Olympics from $1920$ through $2008$ is shown in table.

  

Calculation:

The initial value by the data point $\left(1920,146.6\right)$ and the value after $88$ years by data point $\left(2008,225.8\right)$ .

Calculate the slope of line.

  $\begin{array}{c}m=\frac{225.8-146.6}{2008-1920}\\ =\frac{79.2}{88}\\ =0.9\end{array}$

Using the point slope from the equation.

  $\begin{array}{c}y-146.6=0.9\left(t-20\right)\\ y-146.6=0.9t-18\\ y=0.9t+128.6\\ y\approx t+130\end{array}$

The linear equation is $y\approx t+130$ and the graph is shown below.

  

Therefore, the equation of the line $y\approx t+130$ .

(c)

To determine

The least square regression line that fits the data using regression feature of graphing utility.

Answer to Problem 17E

The equation of the line $y\approx t+130$ .

Explanation of Solution

Given information:

The length (in feet) of the winning men’s discus throws in Olympics from $1920$ through $2008$ is shown in table.

  

Calculation:

Using regression feature of graphing utility.

  

Calculate the equation of least square regression line from above graph.

  $y=1.01t+130.82$

The correlation coefficient for the model is less than $1$ , which implies that the model is a good fit.

Therefore, the equation of least square regression line is $y=1.01t+130.82$ .

(d)

To determine

Compare the linear model in part (b) with the linear model in part (c).

Answer to Problem 17E

The linear model in part (b) with the linear model in part (c) both models are similar.

Explanation of Solution

Given information:

The length (in feet) of the winning men’s discus throws in Olympics from $1920$ through $2008$ is shown in table.

  

Calculation:

By comparing the model found in part (b) $y=t+130$ and the linear model given by graphing utility is $y=1.01t+130.82$ .

From the above observation it is concluded that the both models are similar.

Therefore, the linear model in part (b) with the linear model in part (c)both models are similar.