Question

JUST NEED HELP WITH J AND K THANK YOU!!!:)

Assignment Problem:

Matt Profitt, an MBA student, is studying companies that are going public for the first time. He is curious about whether or not there is a significant relationship between the size of the offering (in millions of dollars) and the price per share.

Size    108     4.4      3.5      8.6      139     228     47.5    5.5      175     12        51        66

Price   12        4          5          6          13        19        8.5      5          15        6          12        12        

a. Develop the appropriate scatterplot for the two variables in the Excel spreadsheet.

b. Based upon the visual inspection of the plot, what type (directional) of relationship do you anticipate between the dependent and independent variables? Offer a brief explanation why that makes theoretical sense.

Please use the example illustrated Tables 12.2 and 12.3 for guidance on the EXCEL steps appropriate to generate the information needed to address the remaining sections.

c. Calculate SS_XX,SS_YY, and SS_XY.

d. Calculate the estimated y intercept (b₀) and the estimated slope coefficient (b₁).

e. Interpret the estimate slope coefficient.

f. Construct the ANOVA appropriate for this regression model.

g. Calculate r².

h. Interpret the coefficient of determination.

i. Calculate s sub b1.

j. Calculate the correlation coefficient.

k. Test whether or not the population correlation coefficient (rho) differs from zero. Use alpha = 0.05.

Answer 1

X	Y	XY	X²	Y²
108	12	1296	11664	144
4.4	4	17.6	19.36	16
3.5	5	17.5	12.25	25
8.6	6	51.6	73.96	36
139	13	1807	19321	169
228	19	4332	51984	361
47.5	8.5	403.75	2256.25	72.25
5.5	5	27.5	30.25	25
175	15	2625	30625	225
12	6	72	144	36
51	12	612	2601	144
66	12	792	4356	144

Ʃx =	848.5
Ʃy =	117.5
Ʃxy =	12053.95
Ʃx² =	123087.07
Ʃy² =	1397.25
Sample size, n =	12
x̅ = Ʃx/n = 848.5/12 =	70.70833333
y̅ = Ʃy/n = 117.5/12 =	9.791666667
SSxx = Ʃx² - (Ʃx)²/n = 123087.07 - (848.5)²/12 =	63091.04917
SSyy = Ʃy² - (Ʃy)²/n = 1397.25 - (117.5)²/12 =	246.7291667
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 12053.95 - (848.5)(117.5)/12 =	3745.720833

j.

Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= 3745.72083/√(63091.04917*246.72917) = 0.9494

k.

Null and alternative hypothesis:

Ho: ρ = 0 ; Ha: ρ ≠ 0

n =12

α = 0.05

Correlation, r =0.9494

Test statistic :  

t = r*√(n-2)/√(1-r²) = 0.9494 *√(12 - 2)/√(1 - 0.9494²) = 9.5575

df = n-2 = 10

Critical value, t_c = T.INV.2T(0.05, 10) = 2.2281

p-value = T.DIST.2T(ABS(9.5575), 10) = 0.0000

Conclusion:

p-value < α Reject the null hypothesis.

There is a enough evidence to conclude that the population correlation coefficient (rho) differs from zero at 0.05 significance level.