Assume a linear statistical relation between Yand X. Using the collected data, a

Question

Assume a linear statistical relation between Yand X. Using the collected data, a simple regression model was estimated and the output is attached For a simple linear "probabilistic relation" the theoretical model that expresses the relation between Y and X is SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Sqar Standard Error Observations 0.854 0.730 0.676 2.173 ANOVA df MS Significance F Regression Residual Total 0.01 63.81 63.81 23.62 4.72 87.43 13.51 6 Coefficien Standard Error t Stat P-value 0.220 0.014 Lower 95% Upper 95% 4.87 0.88 3.48 0.24 -4.06 0.26 13.81 1.49 Intercept 3.68 a. Y = Beta0 Beta1 X b, Y = Beta0 + Beta1 X + Epsilon C. Y Hats Beta0 + Beta1 X d, Y Hat Beta0 + Beta1 X + Epsilon

Explanation / Answer

The simplest deterministic mathematical relationship between two variables x and y is a linear relationship

y = 0 + 1x.

The set of pairs (x, y) for which y = 0 + 1x determines a straight line with slope 1 and y-intercept 0.

But,

The Simple Linear Regression Model There are parameters 0, 1, and 2, such that for any fixed value of the independent variable x, the dependent variable is a random variable related to x through the model equation

Y = 0 + 1x +

The quantity in the model equation is the ERROR -- a random variable, assumed to be symmetrically distributed with E() = 0 and V() = 2.

Hence, Option B

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