91Ó°ÊÓ

Graph the line corresponding to the equation \(y=-2 x+1\) by graphing the points corresponding to \(x=0,1,\) and 2 . Give the \(y\) -intercept and slope for the line. How is this line related to the line \(y=2 x+1\) of Exercise \(12.1 ?\)

What is the difference between deterministic and probabilistic mathematical models?

A Chemical Experiment Using a EX1209 chemical procedure called differential pulse polarography, a chemist measured the peak current generated (in microamperes) when a solution containing a given amount of nickel (in parts per billion) is added to a buffer: \({ }^{2}\) $$ \begin{array}{cc} x=\text { Ni }(\text { ppb }) & y=\text { Peak Current }(\mathrm{mA}) \\ \hline 19.1 & .095 \\ 38.2 & .174 \\ 57.3 & .256 \\ 76.2 & .348 \\ 95 & .429 \\ 114 & .500 \\ 131 & .580 \\ 150 & .651 \\ 170 & .722 \end{array} $$ a. Use the data entry method for your calculator to calculate the preliminary sums of squares and crossproducts, \(S_{x x}, S_{y y},\) and \(S_{x y}\) b. Calculate the least-squares regression line. c. Plot the points and the fitted line. Does the assumption of a linear relationship appear to be reasonable? d. Use the regression line to predict the peak current generated when a solution containing 100 ppb of nickel is added to the buffer. e. Construct the ANOVA table for the linear regression.

What value does \(r\) assume if all the data points fall on the same straight line in these cases? a. The line has positive slope. b. The line has negative slope.

Why is it that one person may tend to gain weight, even if he eats no more and exercises no less than a slim friend? Recent studies suggest that the factors that control metabolism may depend on your genetic makeup. One study involved 11 pairs of identical twins fed about 1000 calories per day more than needed to maintain initial weight. Activities were kept constant, and exercise was minimal. At the end of 100 days, the changes in body weight (in kilograms) were recorded for the 22 twins. \({ }^{16}\) Is there a significant positive correlation between the changes in body weight for the twins? Can you conclude that this similarity is caused by genetic similarities? Explain. $$ \begin{array}{rrr} \text { Pair } & \text { Twin A } & \text { Twin B } \\ \hline 1 & 4.2 & 7.3 \\ 2 & 5.5 & 6.5 \\ 3 & 7.1 & 5.7 \\ 4 & 7.0 & 7.2 \\ 5 & 7.8 & 7.9 \\ 6 & 8.2 & 6.4 \\ 7 & 8.2 & 6.5 \\ 8 & 9.1 & 8.2 \\ 9 & 11.5 & 6.0 \\ 10 & 11.2 & 13.7 \\ 11 & 13.0 & 11.0 \end{array} $$

a. Graph the line corresponding to the equation \(y=-0.5 x+3\) by graphing the points corresponding to \(x=0,1,\) and 2 . Give the \(y\) -intercept and slope for the line. b. Check your graph using the How a Line Works applet. c. How is this line related to the line \(y=0.5 x+3\) of Exercise \(12.76 ?\)