In a simple linear regression, the following information is given: x = - 23; ÿ=
ID: 3159916 • Letter: I
Question
In a simple linear regression, the following information is given: x = - 23; ÿ= 47; Calculate b_1. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Calculate b_0. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) Predict y if x equals -21.(Round intermediate coefficient values and final answer to 2 decimal places.)Explanation / Answer
We will find an equation of the regression line in 4 steps.
Step 1: Find XY and X2 as it was done in the table below.
Step 2: Find the sum of every column:
X=46 , Y=94 , XY=2164 , X2=1060
Step 3: Use the following equations to find a and b:
ab=YX2XXYnX2(X)2=9410604621642106046224=nXYXYnX2(X)2=22164469421060(46)21
Step 4: Substitute a and b in regression equation formula
y y = a + bx= 24 1x
X Y XY XX -24 48 -1152 576 -22 46 -1012 484