podipo Suppose that a teacher wants to study the relationship between the hours

Question

podipo Suppose that a teacher wants to study the relationship between the hours studying and scores on a quiz. The following table presents the hours studying and scores on a quiz tudent Hours Scorex- y-x-2)/s/ sy 1 2.un 2-32 = o.on 1-0.331 5 0.33 1.02 4 2.31 5 3.33 6 Sum and &s;,- = i. (4 pts) Then i = Sx = i. (6 pts) Compute the correlation between hours studying and scores. ii. (5 pts) Interpret the relationship between the hours studying and scores from correlation Coefficient iv. (8 pts) Compute the least-squares regression line for predicting score from hours studying. v. (5 pts) Predict the quiz score of a student who studying 9 hours Page 8 of 9

Explanation / Answer

(i)

Here x = 3.6667 , ybar = 3.3333 , sx = 2.5033 , sy = 1.6330

(ii) Correlation = Zx Zy /(N-1) = 4.3217/ (5-1) = 0.8643

(iii) Here correlation coefficient of 0.8643 is highe and that having positive value so the relationship is positive, strongly linear.

(iv) Here the least square regression line equation

y^ = a + bx

b = r (sy/sx) = 0.8643 * (1.6330/ 2.5033) = 0.5638

a = ybar - bx = 3.3333 - 0.5638 * 3.6667 = 1.266

y^ = 1.266 + 0.5638x

(v) Here x = 9 hours

y^ = 1.266 + 0.5638 * 9 = 6.34

Student Hours Score x- xbar y - ybar Z(x) Z(y) ZxZy 1 1 1 -2.667 -2.333 -1.0652 -1.4289 1.5221 2 1 2 -2.667 -1.333 -1.0652 -0.8165 0.8698 3 3 3 -0.667 -0.333 -0.2663 -0.2041 0.0544 4 4 5 0.333 1.667 0.1332 1.0206 0.1359 5 6 4 2.333 0.667 0.9321 0.4082 0.3805 6 7 5 3.333 1.667 1.3316 1.0206 1.3590 Sum 22 20 0 0 0 0 4.3217 Mean 3.667 3.333 Std/ Dev. 2.5033 1.6330

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