(T or F) Conceptual question: The unexplained variation in the sample is also ca
ID: 2947334 • Letter: #
Question
(T or F) Conceptual question: The unexplained variation in the sample is also called Sum Square of Residuals which represents the lack of fit of the observation on the regression line.
(T or F) Conceptual question: The Least Squares method minimizes the difference of the observed values and the predicted values; therefore, the sum of the errors estimated from the regression line is always zero.
The following data are annual disposable income and total annual consumption for 12 families selected at random from a large metropolitan area. Regard annual disposable income (in U$ 1000) as the explanatory variable and total annual consumption (in U$ 1000) as the dependent variable. Use the SAS output A to answer the question.
The incorrect interpretation of the regression line is (use all decimal places):
A family with no income will have, on average, an annual consumption of U$ 274232.47 dollars.
An increase of U$ 1000 dollars in annual income will increase, on average, U$ 274232.47 dollars in annual consumption.
An increase of U$ 1000 dollars in annual income will increase, on average, U$ 8226.3 dollars in annual consumption.
A family with U$ 56000 income will have, on average, an annual consumption of U$ 48809.6 dollars.
AA family with no income will have, on average, an annual consumption of U$ 274232.47 dollars.
BAn increase of U$ 1000 dollars in annual income will increase, on average, U$ 274232.47 dollars in annual consumption.
CAn increase of U$ 1000 dollars in annual income will increase, on average, U$ 8226.3 dollars in annual consumption.
DA family with U$ 56000 income will have, on average, an annual consumption of U$ 48809.6 dollars.
Quiz 1 SAS Output A Ig The SAS System Obs income cons 1 16000 14000 2 30000 24545 343000 36776Fig. 2 Simple Statistics 4 70000 63254 5 56000 40176 6 50000 49548 7 16000 17000 8 26000 22386 9 14000 16032 10 12000 12000 11 24000 20768 12 30000 34780 Varlable N Mean Std Dev Sum Minimum Maximum Label income 12 32250 18607 387000 12000 70000 in $1000 cons 1229272 15872 351265 12000 63254 in$1000 Pearson Correlation Coefficients, N 12 Prob > Irl under HO: Rho 0 income 1.00000 0.96438 cons 0.96438 F 2577.10795 2577.10795 .0001 19.38649 IR Parameter Estimates Parameter Standard Variable Label DF Estimate Intercept Intercept1 2742.32467 2628.71495 1.04 0.3214 incomein $1000 0.82263 0.07135 Error t Value Pr> tExplanation / Answer
From the parameter Estimates table, we get the regression equation here as:
Annual Consumption = 2742.32467 + 0.82263*(Annual Income )
An increase in Annual income by $1000, the Annual income independent variable increases by 1 unit, which would lead to an increase in U$ 8226.3 dollars in annual consumption.
B is the correct answer here. An increase of US$ 1000 dollars in annual income will increase, on average, U$ 274232.47 dollars in annual consumption, this is incorrect because the increase in variable annual income is not realted to the intercept.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.