We estimate the population variance (sigma-squared) for a multiple regression mo

Question

We estimate the population variance (sigma-squared) for a multiple regression model by using the sample variance (s-squared):   s-squared = SSE / n - (k+1)
What does the denominator ... n - (k+1) ... achieve when calculating this statistic?

Here is a general form multiple regression model ...
y = B0 + B1x1 + B2x2 + B3x3 ... + e

What does "y" represent?
What does the "B2" in the equation mean?
What does the "x2" in the equation mean?
What does the "B3" in the equation mean?
What does the "x3" in the equation mean?
What does "e" represent?

Explain for each of the 4 assumptions what would be the problem for that assumption NOT being true. Assumptions for Random Error e
1.Mean equal to 0
2. Variance equal to ²
3.Normal distribution
4. Random errors are independent (in a probabilistic sense).

Explanation / Answer

n- (k+1) = Indicates the number of independent pieces of information involving the response data needed to
calculate the sum of squares.It is know as degree of freedom.

where n = number of observations and k = number of predictors

Mean square error, which is the variance around the fitted regression line. MS Error = s2. The
formula is:
SS Error/DF Error

y represents observed output, also know as response / dependent variable

B2 represent regression coeffient for independent variable x2

x2 is indepent variable or factor or predicator

B3 represent regression coeffient for independent variable x3.

x3 is indepent variable or factor or predicator

e = error term with a normal distribution, mean of 0, and standard deviation of

Random error e

Normal plot of residuals. The points in this plot should generally form a straight line if the residuals are normally distributed. If the points on the plot depart from a straight line, the normality assumption may be invalid. If your data have fewer than 50 observations, the plot may display curvature in the tails even if the residuals are normally distributed. As the number of observations decreases, the probability plot may show substantial variation and nonlinearity even if the residuals are normally distributed.

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