In a second year economics u, attendance was taken at each ecture during a semes

Question

In a second year economics u, attendance was taken at each ecture during a semester. At the end of the semester, the following equation was estimated using OLS tadard eroms are provided in pareathoees below the piranater estisnatesh final, -55.05 + 0.12 atndrtei, i-1, 300 (3.89) (0.04) R20.0225 where final is the final exam score (out of 100) and atndrtei is the attendance rate (lectures attended as percent of total lectures) for student i. 1.A.2) From the above, we can deduce that the sample correlation coefficient between the final score and the attendance rate is7

Explanation / Answer

To get the sample correlation coefficient we will use the value of R2. R2 is called the coefficient of determination and it is given by the following formula

R2 = explained sum of squares (SSE)/ total sum of squares (SST)

In other words, R2 shows the fraction of the sample variation in the dependent variable that is explained by the independent variable. If one multiplies the value of R2 with 100 then one gets the percentage sample variation in the dependent variable that is explained by the independent variable. This value is obtained by squaring the value of the correlation coefficient.

R2 = (Correlation Coefficient)2

So, to get the value of correlation coefficient we need to take the square-root of the coefficient of determination

Sample Correlation Coefficient = ?R2

Sample Correlation Coefficient = ?0.0225

Sample Correlation Coefficient = 0.15

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