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
1 answer:
Answer:
The answer is OPTION (D)log(y)=0.326x+0.687
<h2>Linear regression:</h2>
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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The equation of the scatter plot is (a) y = 100x + 2
<h3>How to determine the equation of the scatterplot?</h3>The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
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So, we have:
m = 100
The equation is then calculated as:
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This gives
y = 100(x -0) + 2
Evaluate
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