# a. Make a scatterplot for the data in the table below.Height and Weight of Football Players

Question
Scatterplots

a. Make a scatterplot for the data in the table below.
Height and Weight of Football Players
$$\begin{array}{|c|c|}\hline \text{Height (in.):} & 77 & 75 & 76 & 70 & 70 & 73 & 74 & 74 & 73 \\ \hline \text{Weight (lb):} & 230 & 220 & 212 & 190 & 201 & 245 & 218 & 260 & 196 \\ \hline \end{array}$$

b. Which display - the table or the scatter plot - do you think is a more appropriate display of the data? Explain your reasoning.

2021-02-26
Step 1
(a) Scatterplot
Height is on the horizontal axis and Weight is on the vertical axis.
The heights range from 70 to 77, thus an appropriate scale for the horizontal axis is from 69 to 78
The weights range from 190 to 260, thus an appropriate scale for the vertical axis is from 180 to 270.

Step 2
(b) The scatterplot is a more appropriate display of the data, because the relationship between height and weight is more obvious from the scatterplot compared to the table.
For example, we note that the weight tends to increase as the height increases, because the pattern in the scatterplot slopes upwards. However, this fact would have been much harder to derive from the table.
Result:
(a) Height is on the horizontal axis and Weight is on the vertical axis.
(b) Scatter plot.

### Relevant Questions

Make a scatterplot for the data.
Height and Weight of Females
$$\begin{array}{|c|c|}\hline \text{Height (in.):} & 58 & 60 & 62 & 64 & 65 & 66 & 68 & 70 & 72 \\ \hline \text{Weight (lb):} & 115 & 120 & 125 & 133 & 136 & 115 & 146 & 153 & 159 \\ \hline \end{array}$$

Make a scatterplot for the data.
Height and Weight of Females
Height (in.): 58, 60, 62, 64, 65, 66, 68, 70, 72
Weight (lb): 115, 120, 125, 133, 136, 115, 146, 153, 159

Make a scatterplot for each set of data. Tell whether the data show a linear association or a nonlinear association.
$$(1,\ 2),\ (7,\ 9.5),\ (4,\ 7),\ (2,\ 4.2),\ (6,\ 8.25),\ (3,\ 5.8),\ (5,\ 8),\ (8,\ 10),\ (0,\ 0)$$

Make a scatterplot for each set of data.
$$\begin{array}{|c|c|}\hline \text{Hits:} & 7 & 8 & 4 & 11 & 8 & 2 & 5 & 9 & 1 & 4 \\ \hline \text{Runs:} & 3 & 2 & 2 & 7 & 4 & 2 & 1 & 3 & 0 & 1 \\ \hline \end{array}$$

For each set of data below, draw a scatterplot and decide whether or not the data exhibits approximately periodic behaviour.

a) $$\begin{array}{|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline y & 0 & 1 & 1.4 & 1 & 0 & -1 & -1.4 & -1 & 0 & 1 & 1.4 & 1 & 0 \\ \hline \end{array}$$

b) $$\begin{array}{|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 \\ \hline y & 4 & 1 & 0 & 1 & 4 \\ \hline \end{array}$$

c) $$\begin{array}{|c|c|}\hline x & 0 & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 3.5 \\ \hline y & 0 & 1.9 & 3.5 & 4.5 & 4.7 & 4.3 & 3.4 & 2.4 \\ \hline \end{array}$$

d) $$\begin{array}{|c|c|}\hline x & 0 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 12 \\ \hline y & 0 & 4.7 & 3.4 & 1.7 & 2.1 & 5.2 & 8.9 & 10.9 & 10.2 & 8.4 & 10.4 \\ \hline \end{array}$$

Make a scatterplot of the data and graph the function $$\displaystyle{f{{\left({x}\right)}}}=\ -{8}{x}^{{{2}}}\ +\ {95}{x}\ +\ {745}.$$ Make a residual plot and describe how well the function fits the data. $$\begin{array}{|c|c|} \hline \text{Price Increase} & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Sales} & 730 & 850 & 930 & 951 & 1010 \\ \hline \end{array}$$

The following data on = soil depth (in centimeters) and y = percentage of montmorillonite in the soil were taken from a scatterplot in the paper "Ancient Maya Drained Field Agriculture: Its Possible Application Today in the New River Floodplain, Belize, C.A." (Agricultural Ecosystems and Environment [1984]: 67-84):
a. Draw a scatterplot of y versus x.
b. The equation of the least-squares line is 0.45x. Draw this line on your scatterplot. Do there appear to be any large residuals?
c. Compute the residuals, and construct a residual plot. Are there any unusual features in the plot?
$$\begin{array}{|c|c|}\hline x & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\ \hline y & 58 & 34 & 32 & 30 & 28 & 27 & 22 \\ \hline \end{array}$$
$$\displaystyle{\left[\hat{{{y}}}={64.50}\right]}$$.

Use the sample data to construct a scatterplot.
Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation?
The table li sts che t sizes (di stance around chest in inches) and weights (pounds) of anesthetized bears that were measured.
$$\begin{array}{|c|c|}\hline \text{Chest(in.)} & 26 & 45 & 54 & 49 & 35 & 41 & 41 \\ \hline \text{Weight(lb)} & 80 & 344 & 416 & 348 & 166 & 220 & 262 \\ \hline \end{array}$$

1. $$y x\ 5\ 1\ 2.0\ 0.5$$
2. $$y x\ 5\ 1\ 40\ 36.2$$
3. $$y x\ 5\ 25\ 6$$
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