Mr. William Profit is studying companies going public for the first time. He is

Question

Mr. William Profit is studying companies going public for the first time. He is particularly interested in the relationship between the size of the offering and the price per share. A sample of 15 companies that recently went public revealed the following information.

a. Determine the regression equation. (Round your answers to 4 decimal places.)

b-1. State the decision rule for 0.05 significance level: H0: 0;  H1: > 0. (Round your answer to 3 decimal places.)

b-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

b-3. Can we conclude that the slope of the regression line is positive? Use the 0.05 significance level.

c. Determine the coefficient of determination. (Round your answer to 4 decimal places.)

Size Price Size Price ($ millions), per Share, ($ millions), per Share, Company x y Company x y 1 9.0 10.8 9 160.7 11.3 2 94.4 11.3 10 96.5 10.6 3 27.3 11.2 11 83.0 10.5 4 179.2 11.1 12 23.5 10.3 5 71.9 11.1 13 58.7 10.7 6 97.9 11.2 14 93.8 11.0 7 93.5 11.0 15 34.4 10.8 8 70.0 10.7

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 10.666539 + 0.0030171855 x
Sample size: 15
R (correlation coefficient) = 0.46606092
R-sq = 0.21721278
Estimate of error standard deviation: 0.2807859

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) Regression Equation:

y = 10.6665 + 0.0030 x

b - 1) Degrees of freedom = n - 2 = 15 - 2 = 13

Hence,

Critical value = 1.771

So reject Ho if t > 1.771

b - 2) Test statistic = 1.90

b - 3) Since test statistic is not in the rejection region, we do not reject Ho. Hence,

We do not have enough evidence to conclude that the slope of the regression line is positive.

c) Coefficient of determination = 0.2172

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 10.666539 0.14574145 0 13 73.188093 <0.0001 Slope 0.0030171855 0.0015885816 0 13 1.8992953 0.0799

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