In simple linear regression analysis, you make the assumption that the straight

Question

In simple linear regression analysis, you make the assumption that the straight line y = 0 + 1× is the basis for the relationship between the variables and y. The coefficient of determination R2 is a measure of how well the model fits the data. But even when the independent variable does a good job of explaining the variability of the dependent variable, the error variables in the regression model must satisfy certain assumptions, when the assumptions about are seriously violated, the model is not useful for making inferences The assumptions about the error variable are: I. The probability distribution of the is normal 2. The mean of the distribution is 0; that is, E(E) = 0 3. The standard deviation of is , which remains a constant regardless of the value of x 4. The value of associated with any particular value of y is independent of associated with any other value of y The following graph shows the probability distributions of 1 and 2, the error variables for ×1 and ×2, and two values of the independent variable x 0.5 0.4 0.3 0.2 0.1 0.0 1, 2 -2 -1 Based on the graph Assumption 3 is violated Assumption 4 is violated. Assumptions 3 and 1 are violated Assumptions 2 and 4 are violated

Explanation / Answer

Based on the graph:

The probability distribution is not normal & the standard deviation of error terms is not constant.

So here Assumption 1&3 both are violated.

Answer is 3rd option.

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