Question

The table below gives the number of hours ten randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant

Hours studying 0, 1, 1.5, 2, 3, 4, 4.5, 5, 5.5, 6

Midterm grades 60, 61, 72, 76, 80, 81, 88, 89, 91, 96

find the estimated slope round answer to three decimals places

Answer 1

X	Y	XY	X^2	Y^2
0	60	0	0	3600
1	61	61	1	3721
1.5	72	108	2.25	5184
2	76	152	4	5776
3	80	240	9	6400
4	81	324	16	6561
4.5	88	396	20.25	7744
5	89	445	25	7921
5.6	91	509.6	31.36	8281
6	96	576	36	9216

n	10
sum(XY)	2811.60
sum(X)	32.60
sum(Y)	794.00
sum(X^2)	144.86
sum(Y^2)	64404.00
Numerator	2231.60
Denominator	2291.06
r	0.9740
r square	0.9488
Xbar(mean)	3.2600
Ybar(mean)	79.4000
SD(X)	1.3044
SD(Y)	8.4196
b	5.7837
a	60.5450

Slope = 5.784