Question

Please help with questions 1 & 2 with work shown.

PROBLEMS General Problems 1. Using the following information. compute the a, b, and b2 coefficients for the regression of Y on X, and X2, and display the results as a prediction equation: Correlations Standara Deviation X. Variable Mean 1.00 0.60 0.40 -0.30 X. X. 1.00 25 20 1.00 6 2. Compute the beta weights for the data shown in Problem 1, writing out the regression prediction equation for standardized variables.

Answer 1

1. Regression equation : Y = a + b1.x1 + b2.x2

Formulas :



a = у _ bi.fi-b2-T2 = 20-0.8 * 5-(-0.225) * 25-21.625

Regression equation :

y = 21.625 + 0.82.1-0.2252.2

2. Now, standardized variables :

y-y

$x_1' = \frac{x_1-\bar{x_1}}{s_{x_1}}$
$x_2' = \frac{x_2-\bar{x_2}}{s_{x_2}}$
New equation : y' = a + b1'x1' + b2'x2'

Formulas : (Please note that standard deviation of Standardized variable is always 1 and correlation coefficient is independent of change of origin and scale and mean of standardized variables is 0)


r.x;.Y, . Sy . , // 3x, ーー0.3 * 1/1 ー0.3 b2 =

$a=\bar y'-b_1'.\bar{x_1}'-b_2'.\bar{x_2}' = 0-0.4*0-(-0.3)*0 = 0$
Equation : $y'=0.4x_1'-0.3x_2'$