Question

7. The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the standard error of estimate, se, given that Hours (X) 3 5 2 8 2 4 4 5 6 3

Scores (Y) 65 80 60 88 66 78 85 90 90 71

A. 6.305

B. 9.875

C. 8.912

D. 7.913

Answer 1

From the given data, we get the regression equation as below (The same is calculated after the answer.

y' = 56.1139 + 5.0443x

Standard error of the estimate = SQRT {SUM[(y - y')²] / N - 2}. Here N = 10

Calculation of SUM(y - y')². We put each value of x in the regression equation to get y'.

x	y	y'	y - y'	(y - y')2
3	65	71.2468	6.2468	39.02251
5	80	81.3354	1.3354	1.783293
2	60	66.2025	6.2025	38.47101
8	88	96.4683	8.4683	71.7121
2	66	66.2025	0.2025	0.041006
4	78	76.2911	-1.7089	2.920339
4	85	76.2911	-8.7089	75.84494
5	90	81.3354	-8.6646	75.07529
6	90	86.3797	-3.6203	13.10657
3	71	71.2468	0.2468	0.06091
				318.038

Therefore the Se = Sqrt(318.038 / 8) = 6.305 (Option A)

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The Regression Equation:

From the given data, we get:

Count	x	y	xy	x2	y2
1	3	65	195	9	4225
2	5	80	400	25	6400
3	2	60	120	4	3600
4	8	88	704	64	7744
5	2	66	132	4	4356
6	4	78	312	16	6084
7	4	85	340	16	7225
8	5	90	450	25	8100
9	6	90	540	36	8100
10	3	71	213	9	5041
Total	42	773	3406	208	60875

Sum x = 42, Sum y = 773, Sum xy = 3406, Sum x² = 208, (Sum x)² = 1764, n = 10

b1: The slope

b0: The coefficient

Therefore the regression equation = y' = b0 + b1x

y' = 56.1139 + 5.0443x