In: Statistics and Probability
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 SSXX,SSYY, and SSXY.
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.
Could you please just help me with J and K? Thank you so much!
( j )
Find X⋅Y , X2 and Y2 as it was done in the table below.
X | Y | X⋅Y | X⋅X | Y⋅Y |
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 |
correlation coefficient ( r ) = 0.9494
( k )