STATISTICS

Statistics

Statistics

Question 1 (a)

GDP = - 30073 + 84.2 Pop

The interpretation of the coefficient estimates in a multiple regression warrants brief comment. In the model I = a + bE + gX + e, a captures what an individual earns with no education or experience, b captures the effect on income of a year of education, and g captures the effect on income of a year of experience. To put it slightly differently, b is an estimate of the effect of a year of education on income, holding experience constant. Likewise, g is the estimated effect of a year of experience on income, holding education constant.

A multiple regression of GDP and population was highly significant, F (2, 22) = 141.3, p < .001, with both predictor variables being significant in the model. The model accounted for 93% of the variance (r2 = .93). The equation of the model is as follows: 80980 + (712 * GDP) - (1799 * population) (1) where GDP is in billions of US$ purchasing power parity and population is in millions. It is interesting to note in Equation (1) that population has a negative coefficient. The implication is that for a given value of GDP (country wealth), a larger population results in smaller car sales. This is the case because in such a situation, GDP per person (individual wealth) is reduced. If the actual sales were the same as the projected sales, the points would fall on the diagonal line.

The extent of the deviations in above Figure from the diagonal is quantified in Table by presenting the ratios of the actual-to-projected sales. A ratio greater than 1 indicates that the actual sales of new cars in that particular country were greater than the projected sales, and vice versa. The deviations of the ratios in Table 1 from 1 reflect the contributions of factors other than GDP and population size to the demand for personal vehicles.

(ii)

The population variable which is the predictor of the model justifies the equation as the magnitude of probability is 0 which is less than the significant value, so we can suggest that that population can be used as a predictor of GDP. These factors include the cost and availability of gasoline, availability and cost of public transportation, road density, country geography, income homogeneity, population-age distribution, population density, etc. A critical assumption that we made in this study is that the influence of these factors in a given country will remain relatively stable through 2020. We also made the assumption that the influence of these factors on future sales of new cars will be multiplicative. (For example, if in 2006 a country had 120% of the predicted sales, it would continue through 2020 to have 120% of the value derived from the regression Equation (1).) Consequently, in the next analysis we used the ratios in Table 1 as corrections to provide illustrative calculations of 2014 and 2020 sales of new cars based on projected 2014 and 2020 GDPs and ...