Question

23 11. Use the following table to answer the questions Y 7 18 8 10 28 13 32 37 16 41 20 45 26 52 a. Make a scatterplot and determine the relationship between X and Y b. Find the linear regression equation Y' (round a and b to the nearest hundredth) c. Find r and to the nearest hundredth d. Use the equation found in part b to determine X to the nearest whole number when Y' - 60

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Answer 1

Answer:

Given that:

a) Make a scatterplot and determine the relationship between X and Y

The scatterplot is as follows

The relationship between X and Y is positive linear relationship

X	Y
7	18
8	23
10	28
13	32
14	37
16	41
20	45
26	52

Scatterplot with X on X-axis and Yon Y-axis 60 y-1.7478x9.5937 R! -0.9501 50 40 30 20 10 5 10 15 20 25 30

b) Find the linear regression equation Y'

The regression output is as follows

X	Y
7	18
8	23
10	28
13	32
14	37
16	41
20	45
26	52

Summary output:

Regression statistics:

Multiple R	0.9747
R Square	0.9501
Adjusted R square	0.9417
Standard Error	2.7641
Observations	8

ANOVA:

	df	SS	MS	F	Significance F
Regression	1	872.1576	872.1576	114.1508	0.0000
Residual	6	45.8424	7.6404
Total	7	918.0000

	Coefficients	Standard Error	t stat	P-value	Lower 95%	Upper 95%
Intercept	9.5937	2.5277	3.7954	0.0090	3.4086	15.7788
X variable 1	1.7478	0.1636	10.6841	0.0000	1.3475	2.1481

The linear regression equation is

Y=1.7478*x+9.5937

Y=1.75*x+9.59

c) Find r and $r^2$ to the nearest hundredth

r value the multiple R value from the regression statistics section in the above output

So r=0.9747

r =0.97

$r^2$  value is the  R square value from the regression statistics section in the above output

So $r^2$ = 0.9501

$r^2$ =0.95

d)  Use the equation found in part b to determine X to the nearest whole number when Y' = 60

Given $Y'=60$

Y' = 1.7478 * I +9.5937

60 = 1.7478 * r +9.5937

$1.7478*x=60-9.5937$

$1.7478*x=50.4063$

$x=50.4063/1.7478$

$x=28.8398$

$x=28.84$