Question

REGRESSION - USING CALCULATOR

1- You are given data for X_i (independent variable) and Y_i (dependent variable).

2- Calculate the correlation coefficient, r:

3- Calculate the coefficient of determination:

4- Calculate the regression coefficient b₁ (the slope):

5- Calculate the regression coefficient b₀ (the Y-intercept, or constant):

6- The regression equation (a straight line) is:

Problem 2:

A researcher is interested in determining whether there is a relationship between shelf space and number of books sold for her bookstore.

Shelf Space in feet(X)	Books Sold(Y)
7.0	280
3.5	140
4.0	170
4.2	200
4.8	215
3.9	190
4.9	240
7.5	295
3.0	125
5.9	265
5.0	200

Answer 1

	Shelf X	Books Y	X * Y
	7	280	1960	49	78400
	3.5	140	490	12.25	19600
	4	170	680	16	28900
	4.2	200	840	17.64	40000
	4.8	215	1032	23.04	46225
	3.9	190	741	15.21	36100
	4.9	240	1176	24.01	57600
	7.5	295	2212.5	56.25	87025
	3	125	375	9	15625
	5.9	265	1563.5	34.81	70225
	5	200	1000	25	40000
Total	53.7	2320	12070	282.21	519700

r = 0.953

Coefficient of Determination

Explained variation = 0.909* 100 = 90.9%
Unexplained variation = 1 - 0.909* 100 = 9.1%

Equation of regression line is

b = ( 11 * 12070 - 53.7 * 2320 ) / ( 11 * 282.21 - ( 53.7 )^{2})

Slope b = 37.105

a =( 2320 - ( 37.1045 * 53.7 ) ) / 11
Intercept a = 29.772

Equation of regression line becomes

To Test :-

H0 :-

H1 :-

  Test Statistic :-


t = 9.4587

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 9.4587 ) = 0
Reject null hypothesis if P value < level of significance
P - value = 0 < 0.05 ,hence we reject null hypothesis
Conclusion :- We reject H0

There is statistically linear relationship between variables.