Modern medical practice tells us not to encourage babies to become too fat. is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? a random sample of medical files produced the following information for 14 females. x (lb) 23 23 21 26 20 15 25 21 17 24 26 22 18 19 y (lb) 127 122 119 125 130 120 145 130 130 130 130 140 110 115 in this setting we have σx = 300, σy = 1773, σx2 = 6576, σy2 = 225,649, and σxy = 38,186.

a) Figure attached

b)

c) The correlation coefficient would be r =0.47719

d)

Step-by-step explanation:

(a) Draw a scatter diagram for the data.

See the figure attached

(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x

Where:

With these we can find the sums:

And the slope would be:

Nowe we can find the means for x and y like this:

And we can find the intercept using this:

So the line would be given by:

(c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.)

n=14  

And in order to calculate the correlation coefficient we can use this formula:

So then the correlation coefficient would be r =0.47719

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

The % of variation is given by the determination coefficient given by and on this case , so then the % of variation explaines is 22.8%.

(d) If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) ___ lb

So we can replace in the linear model like this: