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# Statistics regression problem samples

10-79
A regression was carried out aimed at assessing the effect of the offer price of an initial public offering (IPO) on the chances of failure of the firm issuing the IPO over various time period from the time of offering ( the maximum length of time being 5 years). The sample was of 2,058 firms, and the regression slope estimates was -0.051> The reported p-value was 0.034. What was the standard error of the slope estimate? Interpret the findings.

10-80
A study was undertaken to find out whether neuroticism affected job performance. The slope estimate of the regression line was 0.16 and r² was 0.19. The sample size was 151. The reported value of the statistical significance of the slope estimate was p< 0.001, two -tailed. Interpret and discuss these findings. Does the degree of "neurosis" affect a worker's performance for the particular jobs studied in this research?

10-82
The following data are operating income X and monthly stock close Y for Clorox, Inc. Graph he data. Then regress log Y on X.
X ( \$millions): 240, 250, 260, 270,280,300, 310,320,330,340,350,360,370,400,420,420,430,450.
Y (\$s): 45,42,44,46,47,50,48,60,61,59,67,75,74,65,95,110,125,130.
Predict Y for X = 305.

10-83
One of several simple linear regression run to assess firm's stock performance based on the Capital Asset Pricing Model (CAPM) for firms with high ratios of cash flow to stock price was the following.
Firm excess return= 0.95 +0.92 Market excess return + Error.
The standard error of the slope estimate was 0.01 and the sample size was 600 (50 years of monthly observations).
a) Is this regression relationship statistically significant?
b) If the market excess return is 1%, predict the excess return for a firm's stock.

10-86
Regress Y against X with the following data from a random sample of the observations:
X Y
12 100
4 60
10 96
15 102
6 68
4 70
13 102
11 92
10 95
18 125
20 134
22 133
8 87
20 122
11 101
a) What is the regression equation?
b) What is the 90% confidence interval for the slope
c) Test the null hypothesis "X does not affect Y" at an &#8049; of 1%
d) Test the null hypothesis "the slope is zero" at an &#8049; of 1%
e) Make a point prediction of Y when X=10
f) Assume that the value of X is controllable. What should be the value of X if the desired value for Y is 100
g) Construct a residual plot. Are the residuals random
h) Construct a normal probability plot. Are the residuals normally distributed.

#### Solution Preview

10-79 Given Slope = -0.051
Sample Size n = 2058
p value = 0.034
From tables of t distribution with 2056 degrees of freedom (that is by using TINV (0.034,2056) function of M.S Excel) we get

We know = 0.0240
Standard Error= 0.0240
Since the p value is less than 0.05 we arrive at the conclusion that the slope coefficient variable is significant at 5% level.
That is, the variation in the offer price of an IPO has significant influence in producing variations in the chances of failure.
10.80 Given Slope = 0.16 ; =0.19 ; Sample Size n = 151 ; p value < 0.001
Since the p value is less than 0.001we arrive at the conclusion that the variable, degree of neurosis, is significant at 0.1% level of significance in explaining worker's performance.
That is the degree of "neurosis" affects significantly, a worker's performance for the particular jobs studied.
At the same time it is to be noted that =0.19. That is, the model explains only 19% of the variations in the worker's performance. This means, variations in the workers performance cannot be explained by using degree of neurosis alone. Because, 81% of the variations are left unexplained. So, more variables are to be included in the ...

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