Question

42 Section Exe Question 1 of 5 (1 point) Attempt 1 of Unlimited Compute the least squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places x 3 2 1 7 4 y 6 2 5 3 4 Regression line equation: y =

Answer 1

here One dependent variable (y) and one independent variable (x) then here we can use simple linear regression model for this the following step we have to compute.

Simple linear regression mathematical model :

Linear Regression refers to a group of techniques for fitting and studying the straight-line relationship between
two variables. Linear regression estimates the regression coefficients β0 and β1 in the equation
Y = β + β X + ε
where X is the independent variable, Y is the dependent variable, β0 is the Y intercept, β1 is the slope, and ε is
the error.

Now the calculation for given data :

X 3 2 1 7 4

Y. 6 2 5 3 4

Sum of X = 17
Sum of Y = 20
Mean X = 3.4
Mean Y = 4
Sum of squares (SSX) = 21.2
Sum of products (SP) = -4

Regression Equation = ŷ = bX + a

b = SP/SSX = -4/21.2 = -0.18868

a = MY - bMX = 4 - (-0.19*3.4) = 4.64151
ŷ = 4.64151 -0.18868X

Now this is the least square regression line for predicting the value of y for given value of x.

Hope you understood then RATE POSITIVE ?.

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