In 1888, Sir Francis Galton published a paper investigating the relationship bet
ID: 3157102 • Letter: I
Question
In 1888, Sir Francis Galton published a paper investigating the relationship between forearm length and height. This paper contained the first published demonstration of the correlation coefficient. Thirty measurements from Galton's data were used to create a regression equation in order to predict a person's height from their forearm length. The analysis produced the following results: y = 26 + 2x SSR = 1095 SSE = 831 Find the correlation coefficient and conduct a test to determine if there is a positive relationship between forearm length and height using alpha = 0.05.Explanation / Answer
a) Compute, SST=SSR+SSE=1095+831=1926
Coefficient of determination, R^2=SSR/SST=1095/1926=0.5685
b) Correlation coefficient, r=sqrt R^2=0.75
H0:p<0 (fore arm length and height are negative correlated)
H1:p>=0 (fore arm and height are positively linearly correlated)
Compute t test statistic,
t=r/sqrt[(1-r^2/n-2]=0.75/sqrt[(1-0.5685)/30-2]=6.03
p value at df=28 (df=n-2) is 0.0000
The p value is less than alpha=0.05. Reject null hypothesis to cocnclude that there is positive linear relationship between forearm length and height.