Answer to Question #317882 in Statistics and Probability for HAN

Question

An emergency service wishes to determine whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown.

Temperature (x) - 25 10 27 30 33

No. of calls (y) - 7 4 8 10 11

a) Find the correlation coefficient r

b) Find the regression equation

c) Graph the regression equation.

Answer 1

$Pearson's\,\,correlation\,\,coefficient:\\n=5\\\sum{x_i}=75\\\sum{y_i}=26\\\sum{{x_i}^2}=3443\\\sum{{y_i}^2}=350\\\sum{x_iy_i}=1094\\a:\\r=\frac{n\sum{x_iy_i}-\sum{x_i}\sum{y_i}}{\sqrt{\left( n\sum{{x_i}^2}-\left( \sum{x_i} \right) ^2 \right) \left( n\sum{{y_i}^2}-\left( \sum{y_i} \right) ^2 \right)}}=\\=\frac{5\cdot 1094-75\cdot 26}{\sqrt{\left( 5\cdot 3443-75^2 \right) \left( 5\cdot 350-26^2 \right)}}=0.997697\\b:\\b=\frac{n\sum{x_iy_i}-\sum{x_i}\sum{y_i}}{n\sum{{x_i}^2}-\left( \sum{x_i} \right) ^2}=\frac{5\cdot 1094-75\cdot 26}{5\cdot 3443-75^2}=0.30371\\a=\frac{\sum{y_i-b\sum{x_i}}}{n}=\frac{26-0.30371\cdot 75}{5}=0.64435$