Many consumer items are marketed to particular age groups in a population. To pl

Question

Many consumer items are marketed to particular age groups in a population. To plan such marketing strategies, it is helpful to know the demographic profile for different areas. Statistics Canada provides a great deal of demographic data organized in different ways. The output below gives regression analysis of the relationship between the percentage of the population over 65 years of age and the percentage under 15 years of age for each of the 13 Canadian provinces and territories. Use it to answer the questions below, as well as the next question. Note that the equation of the regression line is "Fitted Equation" below Fitted Equation: PercentOver65 = 26.19-0.7323 * PercentUnder 15 Estimate Std. Emor t value Prt (intercept) 26.19 PercentUnder 15|-0.7323 12.851 |0.1432 19 iss-tooi -5.11510 0003358 estimated sigma: 2.432 cor(PercentUnder15,PercentOver65): -0.8391 Fitted Plot Residuals Plot 15 15 1. The correlation between the percentage of the population that is over 65 years old and the percentage that is under 15 years old is negative. Explain what a negative correlation means, and why it makes sense that these two variables should be negatively correlated. 2. For each percentage point increase in the percent of residents under 15 years old, how many percentage points do you expect the percent of residents over 65 to change by?

Explanation / Answer

1) Negative correlation means that as one of the variable increases, the other decreases and when that first variable decreases, the other increases. Therefore they are negatively associated with each other. It makes perfect sense here due to the fact that as the total population is constant, as there would be an increase in the percentage of population above the age of 65, there would be an obvious decrease in the percentage of the population in the lower age groups. Therefore the 2 variables are negatively correlated here.

2) Here we are given the regression equation as:

PercentOver65 = 26.19 - 0.7323*PercentUnder15

Clearly as the variable PercentUnder15 increases by a unit percentage point, there would be a decrease in 0.7323% in the percentage population over 65 ( that is equal to the slope coefficient in the equation above )

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