EBK STATISTICS FOR THE BEHAVIORAL SCIEN
EBK STATISTICS FOR THE BEHAVIORAL SCIEN
3rd Edition
ISBN: 9781506386249
Author: PRIVITERA
Publisher: VST
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Chapter 16, Problem 20CAP

1.

To determine

Find the equation of the regression line.

1.

Expert Solution
Check Mark

Answer to Problem 20CAP

The equation of the regression line is, Y^=1.41X+15.43.

Explanation of Solution

Calculation:

The information given that is the psychologist records the time (in minutes) that parents spend with their children during a 20-minute session with the factors birth order (X) time attending to the child (Y).

The procedure of straight line by using the method of least square is shown below:

  • Compute preliminary calculations.
  • Calculate the slope (b).
  • Calculate the y-intercept (a).

The formula for slope is,

slope(b)=SSXYSSX

Where,

SSXY=(XMX)(YMY)

SSX=(XMX)2

In the formulas, MX denotes the mean of factor X, MY denotes the mean of factor Y.

The formula for y-intercept is,

a=MYbMX

The regression equation is, Y^=bX+a.

The value of SSX:

The value of mean for X is,

MX=1+1+5+2+3+2+4+58=238=2.875

XY(XMX)(XMX)2
112(12.875)=1.8753.516
114(12.875)=1.8753.516
59(52.875)=2.1254.516
210(22.875)={0.875}0.766
315(32.875)=0.1250.016
216(22.875)=0.8750.766
48(42.875)=1.1251.266
57(52.875)=2.1254.516
(XMX)2=18.875

Table 1

The value of SSX is 18.875.

The value of SSXY:

The value of mean for Y is,

MY=12+14+9+10+15+16+8+78=918=11.375

XY(XMX)(XMY)
112(12.875)=1.875(1211.375)=0.625
114(12.875)=1.875(1411.375)=2.625
59(52.875)=2.125(911.375)=2.375
210(22.875)={0.875}(1011.375)=1.375
315(32.875)=0.125(1511.375)=3.625
216(22.875)=0.875(1611.375)=4.625
48(42.875)=1.125(811.375)=3.375
57(52.875)=2.125(711.375)=4.375
(XMX)(XMY)
–1.172
–4.922
–5.047
1.203
0.453
–4.047
–3.797
–9.297
(XMX)(XMY)=26.625

Table 2

The value of SSXY is –26.625.

Slope:

Substitute, SSX=18.875 and SSXY=26.625 in slope formula

slope(b)=26.62518.875=1.41

Hence, the value of slope is –1.41.

Substitute, MY=11.375,MX=2.875,b=1.41 in y-intercept formula.

a=MYbMX=11.375(1.41)2.875=11.375+4.054=15.43

Hence, the value of y-intercept is 15.43.

Substitute, a=15.43,b=1.41 in regression equation formula.

Y^=(1.41)X+15.43=1.41X+15.43

The equation of the regression line is, Y^=1.41X+15.43.

2.

To determine

Find the predicted amount of time a parent spends with his or her second-born child.

2.

Expert Solution
Check Mark

Answer to Problem 20CAP

The predicted amount of time a parent spends with his or her second-born child is 12.61 minutes.

Explanation of Solution

Calculation:

The given information is that the amount of time a parent spends with his or her second-born child.

The equation of the regression line is Y^=1.41X+15.43.

Substitute, X=2 in regression line.

Y^=1.41(2)+15.43=2.82+15.43=12.61

Hence, the predicted amount of time a parent spends with his or her second-born child is 12.61 minutes.

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