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x | y | x-xbar | y-ybar | (x-xbar)(y-ybar) | 14 | 2000 | -0.3 | -813.466667 | 244.0400001 | 19 | 9980 | 4.7 | 7166.533333 | 33682.70667 | 20 | 1000 | 5.7 | -1813.466667 | -10336.76 | 9 | 1000 | -5.3 | -1813.466667 | 9611.373335 | 15 | 1560 | 0.7 | -1253.466667 | -877.4266669 | 14 | 6559 | -0.3 | 3745.533333 | -1123.66 | 20 | 800 | 5.7 | -2013.466667 | -11476.76 | 5 | 908 | -9.3 | -1905.466667 | 17720.84 | 14 | 2800 | -0.3 | -13.466667 | 4.0400001 | 21 | 1800 | 6.7 | -1013.466667 | -6790.226669 | 4 | 1325 | -10.3 | -1488.466667 | 15331.20667 | 3 | 1000 | -11.3 | -1813.466667 | 20492.17334 | 16 | 1100 | 1.7 | -1713.466667 | -2912.893334 | 18 | 3261 | 3.7 | 447.533333 | 1655.873332 | 13 | 10282 | -1.3 | 7468.533333 | -9709.093333 | 10 | 8422 | -4.3 | 5608.533333 | -24116.69333 | 10 | 5500 | -4.3 | 2686.533333 | -11552.09333 | 9 | 1178 | -5.3 | -1635.466667 | 8667.973335 | 14 | 1254 | -0.3 | -1559.466667 | 467.8400001 | 6 | 8 | -8.3 | -2805.466667 | 23285.37334 | 12 | 3740 | -2.3 | 926.533333 | -2131.026666 | 35 | 6000 | 20.7 | 3186.533333 | 65961.23999 | 15 | 300 | 0.7 | -2513.466667 | -1759.426667 | 20 | 500 | 5.7 | -2313.466667 | -13186.76 | 8 | 3000 | -6.3 | 186.533333 | -1175.159998 | 16 | 1200 | 1.7 | -1613.466667 | -2742.893334 | 20 | 4241 | 5.7 | 1427.533333 | 8136.939998 | 14 | 1589 | -0.3 | -1224.466667 | 367.3400001 | 7 | 1497 | -7.3 | -1316.466667 | 9610.206669 | 28 | 600 | 13.7 | -2213.466667 | -30324.49334 | | | | | 85023.8 |

How many water bottles do you drink to get though a week? (X) X Bar= 14.3 | Sx =6.988414057 | | |
How many songs do you have on iTunes? (Y) Y Bar= 2813.466667 | Sy = 2843.445782 |

Co-variance S(xy)
= Sum of (x-xbar)(y-ybar)/(n-1)
= 85023.8/29
=2931.85

R(xy) = S(xy)/(Sx)(Sy) = 2931.85/ (6.99)(2843.44)
= 0.1475
There is not much correlation between the two variables
Yhat= b1x-b0 b1 = sum (x-xbar)(y-ybar)/sum(x-xbar)^2 b1 = 85023.8 / 1416.3 b1 = 60.03

b0 = y bar- (b1*x bar) b0 = 2813.466667- (858.429)

Yhat = 60.03x+ 1955.041

SST = SSE + SSR
Sum of (y-ybar)^2 = Sum of (y-yhat)^2 + Sum of (yhat - ybar)^2
234,470,333.5 = 229,366,156+ 5,103,779.955
234,470,333.5 = 234,470,333.5

R square= SSR/SST = 5,103,779.955/ 234,470,333.5 = 0.022
Only about 2.2% of y can v=be explained by the behavior of x

Ho : B1=0
Ha : B1 not = 0

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