Question

Delay Industry Quality Finished Public 62 0 3 1 0 45 0 3 3 1 54 0 2 2 0 71 0 1 2 1 91 0 1 1 0 62 0 4 4 0 61 0 3 2 0 69 0 5 2 1 80 0 1 1 0 52 0 5 3 0 47 0 3 2 0 65 0 2 3 1 60 0 1 3 0 81 1 1 2 0 73 1 2 2 0 89 1 2 1 0 71 1 5 4 0 76 1 2 2 0 68 1 1 2 0 68 1 5 2 0 86 1 2 2 0 76 1 3 1 1 67 1 2 3 0 57 1 4 2 0 55 1 3 2 1 54 1 5 2 0 69 1 3 3 0 82 1 5 1 0 94 1 1 1 0 74 1 5 2 1 75 1 4 3 1 69 1 2 2 0 71 1 4 4 0 79 1 5 2 0 80 1 1 4 0 91 1 4 1 0 92 1 1 4 0 46 1 4 3 1 72 1 5 2 0 85 1 5 1 0 Problem A (Modified from Textbook Ch7 #14) This problem is based on Ch4, #14 in your textbook. Please see this problem on p. 365 for the explanation of the data. But answer the questions below, not the ones in the textbook. Parts (a)(b)(c) here are similar to parts (a)(b)(c) in the textbook. So feel free to check your answers for those parts in the solution you have. a) To see if knowing whether a company is traded on an organized exchange or over-the-counter is helpful in predicting the audit delay, develop a simple regression model to predict audit delay by the dummy variable Public. b) At the 0.05 level of significance, is there a significant relationship between audit delay and Public? (Give your answer in a sentence including your interpretation of the F-test result.) c) Develop the estimated regression equation using all of the independent variables included in the data. d) How much of the variation in the sample values of delay does this estimated regression equation explain? e) At the 0.01 level of significance, is there a significant relationship between audit delay and the combined set of independent variables? (Carefully interpret the F-test result). f) Test the relationship between each independent variable and the dependent variable at the 0.05 level of significance. You will find one independent variable that is not significant. Which variable is this? g) Remove the nonsignificant variable and run a new regression. h) Give the resulting regression equation. Are all the independent variables significant now? Use the regression equation in (h) to answer the remaining questions. i) Predict the audit delay for a public, industrial company whose quality rating is 3 and the “finished” rating is 4. (Hint: Remember you can ignore the given value for a variable that is not included in your regression equation. For example, if the variable “finished” was not significant so was not included in the regression, then its given value 4 will not be used in our calculation.) Express the answer rounded to the first decimal digit. j) According to the regression from (e), is audit delay longer for an industrial company or a non-industrial company? By how many days? k) Suppose company A and B are both non-industrial and have the same “finished” rating, but A’s quality rating is 2 points higher than B’s. Is A’s audit delay longer or shorter than B? By how many days?

Answer 1

The regression analysis between audit delay and dummy variable public is obtained in excel using following steps,

Step 1: Write the data values in excel. The screenshot is shown below.

Step 2: DATA > Data Analysis > Regresion > OK. The screenshot is shown below,

Step 3: Input Y Range: Audit delay column, Input X Range: Public column. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

a)

The regession equation with single explanatory variable, X is defined as,

From the result summary, the regression equation is,

b)

From the result summary, the ANOVA table gives the F statistic value,

and the significance F statistic which is the P-value for the expanatory variable is,

The significance F value > 0.05. The null hypothesis can not be rejected. hence variable pulic donot has a significant effect on audit delay at 5% significance level.

c)

The regression analysis is done in excel similarly as above by selecting all the independent variable column in Input X range. TIck confidence interval and select 99%. The screenshot is shown below,

The result is obtained and screenshot of result summary is shown below,

The regression equation with all independent variables is,

Where X1 is variable Industry, X2 is variable Quality, X3 is variable Finished and X4 is variable Public.

d)

The R square value difines how much of the data fitted with the model. Here R square value is,

The 38.2665% of the audit delay defines by the independent varibles.

e)

From the result summary the Significance F value is,

The significance F value < 0.01 at 5% significance level hence there is a significant relationship between the audit delay and combined set od variables

f)

From the result summary, the P-value defines the significance of the independent variables. The P-values are,

	P-value
Intercept	1.57E-15 < 0.05
Industry	0.0033 < 0.05
Quality	0.0332 < 0.05
Finished	0.03452 < 0.05
Public	0.2625 > 0.05

The P-values are less the 0.05 expect the varible Public has larger P-values. hence all the variables are significant except variable Public at 5% significance level.

g)

After removing the independent variable Public, the regression analysis is done. The screenshot is shown below,

The regression equation is,

h)

All variable have P-value < 0.05 hence all the variables are significant.

i)

The regression equation for variable values is

j)

Audit delay longer for an industrial company than a non-industrial company because for industrial company value "1" adds 12.64531 in the audit delay

k)

A's delay will be shorter beacuse its coefficient is negative.