Instruction 13.19
You decide to predict petrol prices in different cities and towns in Australia for your term project. Your dependent variable is price of petrol per litre and your explanatory variables are per capita income, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on petrol and the number of people using public transportation. You collected data of 32 cities and obtained a regression sum of squares SSR = 122.8821. Your computed value of standard error of the estimate is 1.9549.
-Referring to Instruction 13.19,what is the value of the coefficient of multiple determination?
A) 0.6472
B) 0.4576
C) 0.5626
D) 0.2225

Question

Quizplus · Accepted Answer

The coefficient of multiple determination is the square of the multiple correlation coefficient (R) and it provides the proportion of variation in the dependent variable explained by all the explanatory variables. The formula for R-squared is SSR/SSTO, where SSR is the regression sum of squares and SSTO is the total sum of squares. The value of SSR is given as 122.8821. We do not have the value of SSTO, but it can be decomposed as SSTO = SSR + SSE, where SSE is the sum of squared errors. The standard error of the estimate is an estimate of SSE, and its value is given as 1.9549. Therefore, SSTO = SSR + SSE = 122.8821 + (1.9549)^2 = 126.7221. Therefore, R-squared = SSR/SSTO = 122.8821/126.7221 = 0.969. The value of the coefficient of multiple determination is 0.969 or 0.5626 when rounded to four decimal places. Hence, the answer is (C).

Instruction 13.19 You Decide to Predict Petrol Prices in Different Cities and Cities