Question

Based on the class size and average achievement scores for the five elementary schools in this table, a) calculate the correlation coefficient, r; b) write whether r is positive or negative and strong or weak, c) interpret the correlation, and d) calculate and interpret the coefficient of determination. (Hint: For class size, s = 7.31; for achievement, s = 18.22.)

School	Class Size	Test Score
Main St.	25	80
Casat	14	98
Lakeland	33	50
Shady Grove	28	82
Jefferson	20	90

Answer 1

So, let us answer the questions now-

1) Correlation Coefficient, r = -0.9042

2) r is negative and strong

3) Correlation Coefficient is the degree of relationship between two variables say x and y.

In this case they are strongly negatively correlated which means if one goes up, the other goes down

r= -1 means that the two variables are in perfect opposites. One goes up and other goes down, in perfect negative way

r can range between -1 and 1

4) Coefficient of Determination = r - square = r*r = 0.8175

r-square shows percentage variation in y which is explained by all the x variables together. Higher the better. It is always between 0 and 1

In this case, 81.75% variation in Test scores is explained by the class size as we have considered x to be class size and y to be Test scores

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