Question

Find the linear regression equation for the transformed data. x=1,2,3,4,5 y=13,19,37,91,253 log y=1.114,1.279,1.568,1.959,2,403
A. log(y)=-0.687x+0.326

B. log(y)=0.687x+0.326

C. log(y)=-0.326x+0.687

D. log(y)=0.326x+0.687

Answer 1

Answer:

The answer is OPTION (D)log(y)=0.326x+0.687

Linear regression:

It is a linear model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y)

The Linear regression equation for the transformed data:

We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.

(1, 13) 1.114

(2, 19) 1.279

(3, 37) 1.568

(4, 91) 1.959

(5, 253) 2.403

X            Y           Log(y)

1              13           1.114

2             19         1.740

3             37        2.543

4             91        3.381

5            253      4.226

Sum of X = 15

Sum of Y = 8.323

Mean X = 3

Mean Y = 1.6646

Sum of squares (SSX) = 10

Sum of products (SP) = 3.258

Regression Equation = ŷ = bX + a

b = SP/SSX = 3.26/10 = 0.3258

a = MY - bMX = 1.66 - (0.33*3) = 0.6872

ŷ = 0.3258X + 0.6872

The graph is plotted below:

The linear regression equation is  log(y)=0.326x+0.687

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