The researcher wants to find out if there is any relationship between height of son and his father.He took random sample of fathers and their sons.The summary of the data are given below: summation 6 i=1 xy=24376,mean=60.333,y=67.5, summation 6 i=1 x square =22448, summation 6 i=1 y square=27355
A) Identify which one is dependent and explanatory or independent variable
B)Find the estimates of the parameters
C)Fit the simple linear regression model and interpret it
D) Determine the correlation coefficient and interpret it
A) The father's height is the independent variable and the son's height is the dependent variable.
B) The estimates of the parameters are:
Slope (b) = (24376 - (60.333*67.5))/(22448 - (60.333)^2) = 0.541
Intercept (a) = 67.5 - (0.541*60.333) = -2.919
C) The simple linear regression model is:
Son's Height = -2.919 + 0.541*Father's Height
This model suggests that for every one unit increase in the father's height, the son's height increases by 0.541 units.
D) The correlation coefficient is:
r = (24376 - (60.333*67.5))/sqrt((22448 - (60.333)^2)*(27355 - (67.5)^2)) = 0.845
This suggests that there is a strong positive correlation between the father's height and the son's height.