Question

Which regression model best fits the data set? (2;13); (4;8); (5;7.5); (8;12)

Answer 1

The regression model that best fit the data set is : Y=10.35-0.0467X

Explanation:

The equation of a regression line is given by;

Y=a+bX where b is the slope of the line a is the y-intercept , Y is the dependent variable and X is the independent variable

The slope b is given by;

b = n(∑xy)-(∑x)(∑y) / n(∑x² )-(∑x)²

a=(∑y)(∑x²)-(∑x)(∑xy) /n(∑x²)-(∑x)²

n is the sample size = 4

Form a table as;

x            y               xy             x²              y²

2            13              26            4              169

4             8               32            16            64

5             7.5            37.5          25         56.25

8              12              96           64           144

19             40.5          191.5        109         433.25--------sum

a=(∑y)(∑x²)-(∑x)(∑xy) /n(∑x²)-(∑x)²

a=(40.5)(109) - (19)(191.5) / 4(109) - (19)²

a=(4414.5 - 3638.5) / (436-361)

a=776/75

a=10.35

b = n(∑xy)-(∑x)(∑y) / n(∑x² )-(∑x)²

b=4(191.5)-(19)(40.5) / 4 (109)-19²

b=766-769.5 /436-361

b=-3.5/75

b= - 0.04667

The model will be represented by the equation;

Y=10.35 -0.0466X

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Regression Model: brainly.com/question/10209928

Keyword : regression, model, best fit, data set

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