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 0 2 2 4 4 6 (a) xequals=3 hours (b) xequals=4.5 hours Test score, y 38 40 53 47 62 70(c) xequals=12 hours (d) xequals=3.5 hours Find the regression equation. ModifyingAbove y with caretyequals=nothingxplus+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 = 36.393939 + 5.0909091 x
Sample size: 6
R (correlation coefficient) = 0.84991689
R-sq = 0.72235872
Estimate of error standard deviation: 7.4018835

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	36.393939	5.6164523	? 0	4	6.4798805	0.0029
Slope	5.0909091	1.5780869	? 0	4	3.2260006	0.0321

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	570.18182	570.18182	10.40708	0.0321
Error	4	219.15152	54.787879
Total	5	789.33333

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
3	51.666667	3.0218063	(43.276788, 60.056546)	(29.469133, 73.8642)
4.5	59.30303	3.8385699	(48.645452, 69.960609)	(36.152989, 82.453071)
3.5	54.212121	3.1231239	(45.540939, 62.883303)	(31.906745, 76.517497)

Hence,

Regression equation:

= 5.091 x + 36.39

a) y = 51.7

b) y = 59.3

c) Not meaningful

d) y = 54.2