Instruction 13-7
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 13-7,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, denoted by R-squared, measures the proportion of the total variation in the dependent variable that is explained by the independent variables included in the model. It is calculated as SSR/SST, where SST is the total sum of squares. Since the value of SSR is given as 122.8821, we need to determine the value of SST to calculate R-squared. Unfortunately, SST is not given in the question, so we cannot calculate R-squared exactly. However, we know that R-squared always takes on a value between 0 and 1, and the closer it is to 1, the stronger the relationship between the independent variables and the dependent variable. Therefore, we can eliminate options D) and B) which have very low R-squared values. Option A) has a relatively high R-squared value which suggests that the independent variables have moderate predictive power for petrol prices. However, the best choice is C) 0.5626, which has the highest R-squared value and suggests that the independent variables explain more than half of the variation in petrol prices.

Instruction 13-7 You Decide to Predict Petrol Prices in Different Cities and Cities