Question

The university medical unit is collecting data on the heights (in inches) and weights (in pounds) of the female students on campus. A random sample of ten female students showed the following heights and Height (Inches) Weight (pounds) 60 110 115 110 125 135 145 140 145 150 155 62 63 64 67 68 70 10 Perform a regression analysis (as described on the handout) on this data. TAT 4.3 Problem Hw
Plz help

Answer 1

$\small \begin{tabular}{rrrrr} \hline X & Y & XY & XX & YY \\ \hline 60 & 110 & 6600 & 3600 & 12100 \\ 60 & 115 & 6900 & 3600 & 13225 \\ 62 & 110 & 6820 & 3844 & 12100 \\ 63 & 125 & 7875 & 3969 & 15625 \\ 63 & 135 & 8505 & 3969 & 18225 \\ 64 & 145 & 9280 & 4096 & 21025 \\ 66 & 140 & 9240 & 4356 & 19600 \\ 67 & 145 & 9715 & 4489 & 21025 \\ 68 & 150 & 10200 & 4624 & 22500 \\ 70 & 155 & 10850 & 4900 & 24025 \\ \hline \end{tabular} \\ \sum X =643.0, \sum Y =1330.0\\ \sum XY =85985.0, \sum XX =41447.0, \sum YY =179450.0$
a)

$\small \\ \hat y = a + bx \\ a = \frac{\sum Y * \sum XX-\sum X*\sum XY}{n\sum X^2 -(\sum X)^2} \\ a = \frac{1330.0*41447.0 - 643.0*85985.0}{10*41447.0 - 643.0*643.0} \approx -160.475 \\ b = \frac{n\sum XY -\sum X*\sum Y}{n\sum X^2 -(\sum X)^2} \\ b = \frac{10*85985.0 - 643.0*1330.0}{10*41447.0 - 643.0*643.0} \approx 4.5642 \\ \hat y = -160.475+4.5642x$
b)

$\small \\ r = \frac{n\sum XY -\sum X*\sum Y}{\sqrt{\left(n\sum X^2 -(\sum X)^2\right)\left(n\sum Y^2 -(\sum Y)^2\right)}} \\ r = \frac{10*85985.0 - 643.0*1330.0}{ \sqrt{(10*41447.0 - 643.0^2)(10*179450.0 - 1330.0^2)}} \approx 0.9115$
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