Question

Height	Weight	Age	Shoe Size	Waist Size	Pocket Change
64	180	39	7	36	18
66	140	31	9	30	125
69	130	31	9	25	151
63	125	36	7	25	11
68	155	24	8	31	151
62	129	42	6	32	214
63	173	30	8	34	138
60	102	26	6	25	67
66	180	33	8	30	285
66	130	31	9	30	50
63	125	32	8	26	32
68	145	33	10	28	118
75	235	44	12	40	60
68	138	43	8	27	50
65	165	55	9	30	22
64	140	24	7	31	95
78	240	40	9	38	109
71	163	28	7	32	14
68	195	24	10	36	5
66	122	33	9	26	170
53	115	25	7	25	36
71	210	30	10	36	50
78	108	23	7	22	75
69	126	23	8	24	175
77	215	24	12	36	41
68	125	23	8	30	36
62	105	50	6	24	235
69	126	42	9	27	130
55	140	42	8	29	14
67	145	30	8	30	50

1. weight vs. age α ̇=.01/2

Step 1:                       Ho:    __   _   ___

                                   Ha:    __   _ ___

Step 2:                       Alpha level = _____

Step 3:           Sampling distribution is df = _____

Step 4:           Decision Rule: I will reject the Ho if the |_robs_| value falls at or beyond
                          the |_rcrit_| of ____, otherwise I will fail to reject

Step 5:           Calculation: \_robs_/ = _____

Step 6:           Summary: Since the |_robs_| of ____     _____________ the |_rcrit_| of

                       _____, I therefore reject/fail to reject (choose one) the Ho.

Step 7:           Conclusion: Since _______ occurred, I conclude ___________________________________________________________________.

2. height vs. shoe size α ̇=.02/2

Step 1:                       Ho:    __   _   ___
                                   Ha:    __   _ ___

Step 2:                       Alpha level = _____

Step 3:           Sampling distribution is df = _____

Step 4:           Decision Rule: I will reject the Ho if the |_robs_| value falls at or beyond
                          the |_rcrit_| of ____, otherwise I will fail to reject

Step 5:           Calculation: \_robs_/ = _____

Step 6:           Summary: Since the |_robs_| of ____     _____________ the |_rcrit_| of

                       _____, I therefore reject/fail to reject (choose one) the Ho.

Step 7:           Conclusion: Since _______ occurred, I conclude ___________________________________________________________________.

3.Explain the correlation coefficient of determination.

Answer 1

I have used R software

Enter the data in Excel - save it as comma delimited

The in R use the following syntax

> data=read.csv(file.choose(),header = TRUE) #to import data from excel   
> attach(data) #To attach the imported data in R

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(1)

Let be the population correlation

alpha level =0.01

I have used the test in R as follows

From the above

Sampling distribution is df =28

I will reject H₀ if the observed value of the test statistic |r_obs| falls at or beyond the critical value r_crit,else i will accept .

The test statistic:

where r=sample correlation

n=sample size.

From the R output

r=0.110044 ,n=28

So,

|r_obs| = 0.5859

From t table

As

or,

We fail to reject H₀

Acceptance of H₀ occured we Can say that Population correaltion is zero,or no correlation between Weight and age

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(2)

Let be the population correlation

alpha level =0.02

I have used the test in R as follows

From the above

Sampling distribution is df =28

I will reject H₀ if the observed value of the test statistic |r_obs| falls at or beyond the critical value r_crit,else i will accept .

The test statistic:

where r=sample correlation

n=sample size.

From the R output

r=0.5508678

n=28

|r_obs| = 3.4926

From the t table

Since

or

,i therefore reject the null hypothesis.

Since rejection occurred we can conclude that Height nad shoe size are correlated.

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(3)

correlation coefficient of determination is square of correlation coefficient.It shows the % variation in dependent variable which is explained by all independent variables together.

It is a statisticsla measure of how close the data are to be fitted in a regression line.

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