Course Notes - Department of Mathematics and Statistics

Next Fred calculated the β 1 :n∑(x i − ¯x)(y i − ȳ)ˆβ 1 =Next Fred calculated the β 0 :i=1n∑(x i − ¯x) 2i=1ˆβ 1 = 439.957811.9043ˆβ 1 = 36.9579ˆβ 0 = ȳ − ˆβ 1¯xˆβ 0 = 44.5 − 36.9579 × 1.6125ˆβ 0 = −15.0946Putting this information together Fred gets the following regressionequation.ŷ = −15.0946 + 36.9579xThis means that for every kilo of dog food you have per day, the sizeof the dog you can feed increases by 36 kilos (or equivalently for everyextra 100g of dog food you have per day, the size of the dog you canfeed increases by 3.6 kilos). To test whether or not this is a good model,Fred decided to calculate the r 2 value.⎛r 2 =⎜⎝⎞n∑(x i − ¯x)(y i − ȳ)i=1n∑ √ ⎟(xi − ¯x) 2 (y i − ȳ) 2 ⎠2r 2 =i=1( 439.9578447.0782r 2 = 0.9684) 2263