Question

hours spent studying x	1	1	2	4	5	5
tet score y	40	42	51	48	61	67

find the equation of the regression line for the given data. Then use the regression equation to predict the value of y for each of the given x values, if meaningful. The number of hours 6 students spent for a test and their scores are shown. a.) x = 2hours b.) x= 4.5 hours c.) x = 15 hrs d.) x = 1.5 hrs        Find the regression equation y (hat) =__x +(__) (Round the slope to three decimal places as needed . Round the y intercept to two decimal places as needed.   Predict the value of y for x =2. a.) 46.6 b.) 44.1 c.) 58.9 d.) not meaningful       Predict the value of of y for x = 4.5. a.) 110.8 b.) 58.9   c.) 44.1 d.) not meaningful.     Predict the value of y for x = 15.   a.) 46.6 b,) 110.8 c.) 58.9 d.) not meaningful. Predict the value of y for x = 1.5   a.) 46.6 b.) 110.8 c.) 44.1   d.) not meaningful

Answer 1

Consider

Y : test Score.

X : Number of hours spends for study.

The regression equation Y on X is

Y = a + b X

where a is Y-intercept and b is slope of the regression line.

The estimated value of a and b is

x	y	(x-xbar)	(y-ybar)	(x-xbar)*(y-ybar)	(x-xbar)^2
1	40	-2	-11.5	23	4
1	42	-2	-9.5	19	4
2	51	-1	-0.5	0.5	1
4	48	1	-3.5	-3.5	1
5	61	2	9.5	19	4
5	67	2	15.5	31	4
18	309	0	0	89	18

Hence the line of regression Y on X is

Y = 4.944X + 36.67.

Value of slope = 4.944 and Y-intercept = 36.67

Predicted value of Y for diffrent value of X is

X	Predicted value of Y	Correct Answer
2	46.558	a- 46.6
4.5	58.918	b- 58.9
15	110.83	b- 110.8
1.5	44.086	c- 44.1