CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 9. Regression and Correlation

Review Answers

1. The predictor variable is the number of years of formal education. The reasoning behind this decision is
   that we are trying to determine and predict the financial benefits of further education (as measured by annual
   salary) by using the number of years of formal education (the predictor, or theX, variable.


2. Yes. With anr-value of 0.67, these two variables appear to be moderately to strongly correlated. The nature
   of the relationship is a relatively strong, positive correlation.
   3.Y= 0. 782 X+ 3. 842


3. ForX= 13. 5 ,Y= 14 .39 or $14, 390


4. (a)H 0 :β= 0 ,Ha:β 6 =0 (b) The critical values are set att=± 1 .98 (c)Sb=

(

√sy∗x

SSx

)

=

(

√^3.^12

1542

)

=

. 08 ,t=b−sbβ=^0.^792. 08 −^0 = 9 .9 (d) Since the calculated test statistic of 9.9 exceeds the critical value of 1.98, we
decide to reject the null hypothesis and can conclude that the if the null hypothesis was true, we would observe
a regression coefficient of 0.792 by chance less than 5% of the time.
6. ForX=15,Yˆ= 15 .57. Therefore, 18.50 has az-value of 0.93:

z=

Y−Y ̈

sY∗X

=

18. 5 − 15. 57

3. 12

= 0. 93

Thez-value of 0.936 has a correspondingp-value of.1677. This means that with 15 years of formal education,

an estimated 16.77% of the parents will have an income greater than $18, 500

7. ForX=12,Yˆ= 13 .2. Therefore, 18.50 has az-value of 0.93:

z=

Y−Y ̈

sY∗X

=

18. 5 − 13. 25

3. 12

= 1. 68

Thez-value of 0.936 has a correspondingp-value of.0465. This means that with 15 years of formal education,

an estimated 4.65% of the parents will have an income greater than $18, 500

8.sYˆ=sY∗X

√

1 +

1

n

+

(X−Xˆ)^2

SSx

= 3. 12

√

1 +

1

120

+

( 16 − 14. 85 )^2

1542

= 3. 14

Using the general formula for the confidence interval(CI=Yˆ±(tcvsY)), we find that

CI 95 = 16. 35 ±( 1. 98 )( 3. 14 ) = 16. 35 ± 6. 22

CI 95 = ( 10. 13 , 22. 57 )

9. Answer is to the discretion of the teacher.