Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.

# Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.

393k points

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

Hours spent studying, x 1 2 3 4 4 5
Test score, y 42 47 52 50 62 69

(a) x = 3 hours
(b) x = 3.5 hours
(c) x = 12 hours
(d) x = 4.5 hours

linear regression
scatter plot

100 points

how did you get 161/3?

403.4k points

The find the line of regression use the following equations,

$$m = \frac{\bar{x}\bar{y}-\overline{xy}}{(\bar{x})^2-\overline{x^2}}$$

$$b = \bar{y}-m\bar{x}$$

$$\hat{y} = mx+b$$

now it is only a matter of finding $\bar{x}, \bar{y}, \overline{xy},\text{ and }\overline{x^2}$. So,

$$\bar{x}=\frac{1+2+3+4+4+5}{6}=\frac{19}{6}$$

$$\bar{y}=\frac{42+47+52+50+62+69}{6}=\frac{161}{3}$$

$$\overline{xy}=\frac{1(42)+2(47)+3(52)+4(50)+4(62)+5(69)}{6}=\frac{1085}{6}$$

$$\overline{x^2}=\frac{1^2+2^2+3^2+4^2+4^2+5^2}{6}=\frac{71}{6}$$

plugging these values into $m$ and $b$ gives,

$$m=\frac{(19/6)(161/3)-(1085/6)}{(19/6)^2-71/6}=\frac{392}{65}\approx 6.031$$

$$b=\frac{161}{3}-\frac{392}{65} \frac{19}{6}=\frac{2247}{65} \approx 34.569$$

and hence the line of regression is,

$$\hat{y}=6.031x+34.569$$

by plugging in the x values you will obtain the test score for any value of x. Remember that if the test score is above 100 that would be viewed as not meaningful.

Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$

Use LaTeX to type formulas and markdown to format text. See example.

• Answer the question above my logging into the following networks

### Post as a guest

• Your email will not be shared or posted anywhere on our site
•

Stats
Views: 3.1k