Question

1. correlation

It is interested to investigate if there is an association between body weight and the concentration of cholesterol in the blood. Subjects were randomly selected from a population of adult males between the ages of 50 and 55 with a height of between 60 and 69 inches in height. the data appears in the following table

weight (pounds) X	cholesterol (mg/100 ml) Y
146	181
205	228
157	182
165	249
184	259
153	201
220	339
181	224
151	112
188	241
181	225
163	223
198	257
193	337
157	197

Use an alpha level of 0.01. Determine if the exercises are effective in reducing weight.

please use the answer format sheet for better understanding of the exercise and show the calculation to understand from were the results came, thank you very much in advance.

Answer sheet

situation #1

Data:

Hypothesis: Ho: Ha:

mathematical model:

Decision:

Conclusion:

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	2642.00	3455.00	6873.73	46053.33	13967.33
mean	176.13	230.33	SSxx	SSyy	SSxy

sample size ,   n =   15          
here, x̅ = Σx / n=   176.133   ,     ȳ = Σy/n =   230.333  
               1.307721423  
SSxx =    Σ(x-x̅)² =    6873.7333          
SSxy=   Σ(x-x̅)(y-ȳ) =   13967.3          
                  
estimated slope , ß1 = SSxy/SSxx =   13967.3   /   6873.733   =   2.03199
                  
intercept,   ß0 = y̅-ß1* x̄ =   -127.56722          
                  
so, regression line is   Ŷ =   -127.5672   +   2.0320   *x
------------

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   15  
alpha,α =    0.01  
correlation , r=   0.7850  
t-test statistic = r*√(n-2)/√(1-r²) =        4.57
DF=n-2 =   13  
p-value =    0.0005  
Decison:   p value < α , So, Reject Ho