Question

1) What is the sum ∑ X Y?

2) What is the Pearson correlation coefficient (r) for the data below?

3)If you were to test the Pearson correlation coefficient for significance, what would be the critical value of t (alpha=.05)?

4) If you were to test the Pearson correlation coefficient for significance, what would be the computed value of t (alpha=.05)?

5)If you were to test the Pearson correlation coefficient for significance, what would be your conclusion (alpha=.05)?

6) For the data below, what is the value of "b" for the regression equation?

7)For the data below, what is the value of "a" for the regression equation?

8)For the data below, what is the IQ of the son if the father has an IQ of 100?

9)For the data below, what is the IQ of the son if the father has an IQ of 90?

10) For the data below, what is the IQ of the son if the father has an IQ of 80

11) For the data below, what is the standard error of the estimate for the previous predictions

Family	Father	Son
	120	121
	110	105
	120	125
	92	87
	85	92
	72	90
	107	110
	115	122
	155	133
	90	123

Answer 1

X	Y	XY	X²	Y²
120	121	14520	14400	14641
110	105	11550	12100	11025
120	125	15000	14400	15625
92	87	8004	8464	7569
85	92	7820	7225	8464
72	90	6480	5184	8100
107	110	11770	11449	12100
115	122	14030	13225	14884
155	133	20615	24025	17689
90	123	11070	8100	15129
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
1066	1108	120859	118572	125226

Sample size, n =	10
x̅ = Ʃx/n = 1066/10 =	106.6
y̅ = Ʃy/n = 1108/10 =	110.8
SSxx = Ʃx² - (Ʃx)²/n = 118572 - (1066)²/10 =	4936.4
SSyy = Ʃy² - (Ʃy)²/n = 125226 - (1108)²/10 =	2459.6
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 120859 - (1066)(1108)/10 =	2746.2

1) Ʃxy = 120859

2) Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 2746.2/√(4936.4*2459.6) = 0.7881

3) df = n-2 = 8

Critical value, t_c = T.INV.2T(0.05, 8) = 2.3060

4) t = r*√(n-2)/√(1-r²) = 0.7881 *√(10 - 2)/√(1 - 0.7881²) = 3.6216

5) Conclusion :

t = 3.8216 > 2.3060, Reject the null hypothesis. There is a correlation between x and y.

6) Slope, b = SSxy/SSxx = 2746.2/4936.4 = 0.55632

7) y-intercept, a = y̅ -b* x̅ = 110.8 - (0.55632)*106.6 = 51.49668

8) Predicted value of y at x =    100

ŷ = 51.4967 + (0.5563) * 100 = 107.13  

9) Predicted value of y at x =    90

ŷ = 51.4967 + (0.5563) * 90 = 101.57   

10) Predicted value of y at x =    80

ŷ = 51.4967 + (0.5563) * 80 = 96.00

11)Sum of Square error, SSE = SSyy -SSxy²/SSxx = 2459.6 - (2746.2)²/4936.4 = 931.84406

Standard error of estimate, se = √(SSE/(n-2)) = √(931.84406/(10-2)) = 10.79261