Question

Is there a correlation between mean course grade and mean attendance in data set 7176? What is the equation of the regression line? What is the best prediction for a mean attendance of 80%?

Class 7176
Unit Test 3	Course Grade	Attendance
238	63	96
208	55	48
258	89	96
264	84	96
324	98	100
0	62	44
0	56	66
274	87	96
274	83	96
0	0	18
179	71	100
268	86	100
241	60	87
0	8	26
278	84	96
307	89	87
294	87	100
175	76	74
129	66	87
284	82	100
297	90	79
255	74	74
268	88	100
215	77	39
146	71	87
304	88	100

Answer 1

Hence we see there is positive trend hence positive correlation between x and y

x-Mx	y-My	(x-Mx)^2	(x-Mx)(y-My)
-9.0769	15.5385	82.3905	-141.0414
-17.0769	-32.4615	291.6213	554.3432
16.9231	15.5385	286.3905	262.9586
11.9231	15.5385	142.1598	185.2663
25.9231	19.5385	672.0059	506.497
-10.0769	-36.4615	101.5444	367.4201
-16.0769	-14.4615	258.4675	232.497
14.9231	15.5385	222.6982	231.8817
10.9231	15.5385	119.3136	169.7278
-72.0769	-62.4615	5195.083	4502.0355
-1.0769	19.5385	1.1598	-21.0414
13.9231	19.5385	193.8521	272.0355
-12.0769	6.5385	145.8521	-78.9645
-64.0769	-54.4615	4105.852	3489.7278
11.9231	15.5385	142.1598	185.2663
16.9231	6.5385	286.3905	110.6509
14.9231	19.5385	222.6982	291.574
3.9231	-6.4615	15.3905	-25.3491
-6.0769	6.5385	36.929	-39.7337
9.9231	19.5385	98.4675	193.8817
17.9231	-1.4615	321.2367	-26.1953
1.9231	-6.4615	3.6982	-12.426
15.9231	19.5385	253.5444	311.1124
4.9231	-41.4615	24.2367	-204.1183
-1.0769	6.5385	1.1598	-7.0414
15.9231	19.5385	253.5444	311.1124
		SS: 13477.8462	SP: 11622.0769

Sum of X = 1874
Sum of Y = 2092
Mean X = 72.0769
Mean Y = 80.4615
Sum of squares (SS_X) = 13477.8462
Sum of products (SP) = 11622.0769

Regression Equation = ŷ = bX + a

b = SP/SS_X = 11622.08/13477.85 = 0.8623

a = M_Y - bM_X = 80.46 - (0.86*72.08) = 18.3089

ŷ = 0.8623X + 18.3089

For x=80, ŷ = 0.8623*80 + 18.3089=87.2929