Question

could someone please help me solve this and show the steps in the calculator as well?? thank you!!

2. The following information is gathered from a bivariate dataset: Xbar = 12, sx - 3, ybar = 60, sy = 7.5, r=-0.8. (a) Write the equation of the least-squares regression line. (b) What fraction (percentage) of the variation in y is explainable by variation in x? (c) An individual data pair is (15, 49). State the residual for that data pair. son in x?

Answer 1

Equation of regression line is y^=b_{​​​​​​0} + b₁x.

Where b_{​​​​​​1}​​​=r.s_y/s_{​​​​​x}

b_{​​​​​​0} = ybar-b₁.xbar

Residual is the difference between actual y value and the predicted y value =y-y^.

as Equation of the least squares regression line u ý = borbia where bi & sy to 5 - 72 bo - g-bin 60-(-2x 12) = 184 - 0.88 7.5 sx て y 84-22 b variation of that ů as The percentage the the variation explained by e en x= 10082 = 100x (0-8)" 0.64 164 % G Given data Pau Caly) = (15,49) At x=15 the predicted value 84-22 +84-2015) 54 ie At x=15, = 49, 54 Residual ly } [49-54) = -5 & residual 5