The purpose of the adjusted multiple coefficient of determination in multiple li

Question

The purpose of the adjusted multiple coefficient of determination in multiple linear regression is to a. adjust predictions b. adjust R^2 for impact of additional error in estimation c. adjust slope of R^2 d. adjust R^2 for impact of additional independent variables The purpose of the t test in multiple regression is to test for a. independence of variables b. statistical significance of independent variables c. multicollinearity d. statistical significance of the overall model Suppose an estimated regression equation is given by y = 210 + 3x_1 - 15x_2 where y is measured in thousands of dollars, x_1, is measured in thousands of dollars, and x_2 is measured in years. a. If x_1 is held constant and x_2 is increased by 2 years, what will be the exact change in y? Indicate units in your answer. b. If x_2 is held constant and x_1 is increased by $500, what will be the exact change in y? Indicate units in your answer. c. To the nearest hundredth, what exactly is y when x_1 = $2,000 and x_2 = 10 years? Indicate units in your answer. The primary purpose of residual analysis is to assess a. stability of error terms b. statistical significance of independent variables c. goodness of model fit d. statistical significance of the overall model In multiple regression involving 3 independent variables, the basic relationship involving SSR, SSE, and SST is a. 3SSR + 3SSE = SST b. undefined c. SSR + SSE = SST/3 d. SSR + SSE = SST

Explanation / Answer

The answer of first question is (d)

Because it measure the impact of addition of new independent if it actually importand to predict the dependent variable then R^2 adjusted increase. If the new independent variable is not important then R^2 adjusted is not increase. So the answer of first question is (d)

For second question the correct answer is (b)

Because t test in multiple regression model help us to find the significance of the corresponding independent variable. If the null hypothesis H0 is reject then its corresponding variable is important that is its coefficient is not equal to zero.

If null hypothesis accepted then its coefficient may be zero and its corresponding variable is not important to predict the dependent variable.

3) a) Since x1 is constant and x2 is increase by 2 years and the slope of x2 is -15 so there is decrease in mean of dependent variable y is 2*15 = 30 thousand dollars.

b) similarly here x2 is constant and slope of x1 is 3 therefore increase of $500 in x1 also increase in mean variable y is = 3*500 = 1500 dollar.

c) y = 210 +(3*2000) - (15 *10) = $6060 = 6100 (after rounding up to nearest hundread).

Question #4 We can use residual analysis mainly for the checking of model inadequacy .

Also we can use it to check the assumptions of the models such as constant variance, normalyty assumption, randomness of the dependent variable etc.

So correct answer of it asd) statistical significance of overall model

The answer of last question is d) because total sum of square(SST) is always equal to regression sum of square(SSR) and error sum of square(SSE)

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