Question

Please help with multi step question- 1 question with 6 parts!!

The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, y bo + bix, 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 0.5 2.5 3 4 4.5 5 5.5 Midterm Grades62 74 86 87 97 98 100 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. AnswerHow to Enter) 2 Points KeypadTables Nex Prev

Answer 1

Solution:

We have formulas given as below:

Slope = b₁ = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

y-intercept = b₀ = Ybar – b*Xbar

Calculation table is given as below:

No.	X	Y	X^2	Y^2	XY
1	0.5	62	0.25	3844	31
2	2.5	74	6.25	5476	185
3	3	86	9	7396	258
4	4	87	16	7569	348
5	4.5	97	20.25	9409	436.5
6	5	98	25	9604	490
7	5.5	100	30.25	10000	550
Total	25	604	107	53298	2298.5

Xbar = ∑X/n = 25/7 = 3.571429

Ybar = ∑Y/n = 604/7 = 86.28571

b₁ = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

b₁ = (2298.5 - 7*3.571429*86.28571)/( 107- 7*3.571429^2)

b₁ = 7.97984

Slope = 7.97984

b₀ = Ybar – b*Xbar

b₀ = 86.28571 - 7.97984*3.571429

b₀ = 57.78628

y-intercept = 57.78628

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = [7*2298.5- 25*604]/sqrt[(7*107– 25^2)*(7*53298– 604^2)]

r = 0.97713

Coefficient of determination = r^2 = 0.97713*0.97713 = 0.954783

Answers:

Step 1

Answer:

Slope = 7.980

Step 2

Answer:

y-intercept = 57.786

Step 3

Answer: 93.696

We are given X = 4.5

We have

Y = 57.786 + 7.980*X

Y = 57.786 + 7.980*4.5

Y = 93.696

Step 4

Answer: b₁

Step 5

Answer: 3.304

Error = Residual = Observed – predicted

When x = 4.5

Observed = 97

Predicted = Y = 57.786 + 7.980*X

Predicted =Y = 57.786 + 7.980*4.5

Predicted = 93.696

Error = Residual = 97 - 93.696

Error = Residual = 3.304

Step 6

Answer: 0.955