5. A researcher is interested in the relationship between water consumption and productivity. Sherecords the amount of water consumed along with the number of hours spent studying fourparticipants. The data for this hypothetical study is listed in the table below.Water Consumption Productivity(in ounces)(in hours)8.4168.206.2810a. Compute the correlation for this datab. What is the predictor?c. What is the criterion?d. Compute the regression equation for this datae. What percentage of the variance in productivity is accounted for the ounces of waterconsumption?f. What is the predicted number of productivity hours for someone who consumes 36 ounces ofwater?g. Sketch a scatterplot of the data. Overlay the regression line onto the scatter plot.

Answered: a. Compute the correlation for this…

MATLAB: An Introduction with Applications

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5. A researcher is interested in the relationship between water consumption and productivity. She
records the amount of water consumed along with the number of hours spent studying four
participants. The data for this hypothetical study is listed in the table below.
Water Consumption Productivity
(in ounces)
(in hours)
8.
4
16
8.
20
6.
28
10
a. Compute the correlation for this data
b. What is the predictor?
c. What is the criterion?
d. Compute the regression equation for this data
e. What percentage of the variance in productivity is accounted for the ounces of water
consumption?
f. What is the predicted number of productivity hours for someone who consumes 36 ounces of
water?
g. Sketch a scatterplot of the data. Overlay the regression line onto the scatter plot.

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The sums are,

Water consumption (x)	Productivity (y)	$x^{2}$	$y^{2}$	xy
8	4	64	16	32
16	8	256	64	128
20	6	400	36	120
28	10	784	100	280
$\sum_{} x = 72$	$\sum_{} y = 28$	$\sum_{} x^{2} = 1504$	$\sum_{} y^{2} = 216$	$\sum_{} x y = 560$

The correlation coefficient is,

$\begin{array}{rcl} r & = & \frac{n \sum_{} x y - (\sum_{} x) (\sum_{} y)}{\sqrt{[n \sum_{} x^{2} - {(\sum_{} x)}^{2}] [n \sum_{} y^{2} - {(\sum_{} y)}^{2}]}} \\ = & \frac{(4 \times 560) - (72 \times 28)}{\sqrt{[(4 \times 1504) - {(72)}^{2}] [(4 \times 216) - {(28)}^{2}]}} \\ = & \frac{224}{257.9922} \\ = & 0.8682 \end{array}$

Thus, the correlation coefficient is 0.8682.

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