# Straight Lines Graph the straight lines in Exercises 1–3.Then find the change in y for a one-uni

Question
Scatterplots

Straight Lines Graph the straight lines in Exercises 1–3.
Then find the change in y for a one-unit change in x, find the point at which the line crosses the y-axis, and calculate the value of y when x 52.5.
1. $$y x\ 5\ 1\ 2.0\ 0.5$$
2. $$y x\ 5\ 1\ 40\ 36.2$$
3. $$y x\ 5\ 25\ 6$$
Scatterplots For the scatterplots in Exercises 5 describe the pattern that you see. How strong is the pattern? Do you see any outliers or clusters?

2020-11-30
Step 1
From the given graph, it is observed that, as x increases y also increases so the direction of the graph is positive.
The given graph is linear as it does follow a straight line path with respect to two variables of graph.
Step 2
The strength of given graph is stronger as there are good number of samples along the line of curve.
There are two cluster of points at the bottom side of the graph where multiple points exist along the line. There is two outlier points as it appears out of the range of linear pattern in graph.

### Relevant Questions

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.
$$\begin{array}{|c|c|}\hline \text{Hits:} & 7 & 8 & 4 & 11 & 8 & 2 & 5 & 9 & 1 & 4 \\ \hline \text{Runs:} & 3 & 2 & 2 & 7 & 4 & 2 & 1 & 3 & 0 & 1 \\ \hline \end{array}$$

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?
$$\begin{array}{|c|c|}\hline x & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\ \hline y & 58 & 34 & 32 & 30 & 28 & 27 & 22 \\ \hline \end{array}$$
$$\displaystyle{\left[\hat{{{y}}}={64.50}\right]}$$.

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.

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

The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral.

a) $$\int_{0}^{6}g(x)dx$$
b) $$\int_{6}^{18}g(x)dx$$
c) $$\int_{0}^{21}g(x)dx$$
the graph of g consists of two straight lines and a semicircle. use it to evaluate each integral

a)$$\int_0^{10}g(x)dx$$
b)$$\int_{10}^{30}g(x)dx$$
c)$$\int_0^{35}g(x)dx$$
The accompanying data on y = normalized energy $$\displaystyle{\left[{\left(\frac{{J}}{{m}^{{2}}}\right)}\right]}$$ and x = intraocular pressure (mmHg) appeared in a scatterplot in the article “Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts” (Current Eye Research, 2012: 43-49), an estimated regression function was superimposed on the plot.
$$\begin{array}{|c|c|}\hline x & 2761 & 19764 & 25713 & 3980 & 12782 & 19008 & 19028 & 14397 & 9606 & 3905 & 25731 \\ \hline y & 1553 & 14999 & 32813 & 1667 & 8741 & 16526 & 26770 & 16526 & 9868 & 6640 & 1220 & 30730 \\ \hline \end{array}$$
$$\begin{array}{|c|c|}\hline \text{Predictor Coef SE Coef T P Constant} & -5090 & 2257 & -2.26 & 0.048 \\ \hline \text{Pressure} & 1.2912 & 0.1347 & 9.59 & 0.000 \\ \hline \end{array}$$
$$[S=3679.36, R-Sq = 90.2\%, R-Sq(adj)=89.2\% ]$$.
State the slope and y-intercept of the equation. $$5x + 4y = 20$$