Question

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.

font size decreased by 1 font size increased by 1 Hours spent studying comma xHours spent studying, x

00

22

22

33

44

66

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​(a)

xequals=22

hours

​(b)

xequals=4.54.5

hours

Test​ score, y

4040

4545

5050

4848

6565

7070

​(c)

xequals=1212

hours

​(d)

xequals=3.53.5

hours

Find the regression equation.

ModifyingAbove y with caretyequals=nothing xplus+left parenthesis nothing right parenthesis

​(Round the slope to three decimal places as needed. Round the​ y-intercept to two decimal places as​ needed.)

Answer 1

The statistical software output for this problem is:

Simple linear regression results:

Dependent Variable: y
Independent Variable: x
y = 37.632 + 5.424 x
Sample size: 6
R (correlation coefficient) = 0.9357289
R-sq = 0.87558857
Estimate of error standard deviation: 4.6660476

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	37.632	3.4667195	≠ 0	4	10.855219	0.0004
Slope	5.424	1.0222798	≠ 0	4	5.3057881	0.0061

Hence,

Regression equation will be:

y = 5.424 x + 37.63