SINTERPRETATIONS: Say you wanted to understand the factors that are related to a

Question

SINTERPRETATIONS: Say you wanted to understand the factors that are related to a ntry's Life Expectancy ick a quantitative variable that you think may have an association with Life Expectancy explain why you think the association exists. ne student chose to look at the variable Literacy Rate and its association with Life ectancy 1) Assuming there is a linear relationship between Literacy Rate and Life Expectancy and she performed all calculations correctly, explain what an R2 of 64% means. 2) Based on (correctly) calculating the least-squares line. she concluded 'the slope of the least-squares line shows that an increase of 5% in Literacy Rate will produce 2-year improvement in Life Expectancy:' Do you think her conctusion is justified? Why or why not? 3) will all the residuals from the least-squares ine be positive? Explain your reasoning.

Explanation / Answer

Answer:

Part 1

For the given scenario, the value of the R square or coefficient of determination is given as 64% which means about 64% of the variation in the dependent variable life expectancy is explained by the independent variable literacy rate.

Part 2

We know that the slope is interpreted as the rate of change in dependent variable as the independent variable changes. For the given scenario, the conclusion is justified because the slope explains two year improvement in dependent variable life expectancy as increase of 5% in independent variable literacy rate.

Part 3

All the residuals from the least squares line will not be positive because predicted values may be less or greater than the actual values.

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