Statistics Exam Scores And Regression Analysis

Frequency distribution

The class range 70-80 represent the modal class as it has the highest percent frequency distribution.

Question 2

1. Let’s denote the sample size by letter n and the number of regressions by letter k

From the regression output, the value of k is 1

Now using the formula       

This gives n as 41 which is our sample size.

1. In this case we are testing the hypothesis that the coefficient if x is 0.

To attain this will calculate the p value and compare it with the alpha.

The rejection rule is; if p value if less than alpha, we reject the null hypothesis that states that the coefficient of x is 0

Construction of the p value

Being that the p value is greater than the selected alpha

   we fail to reject the null hypothesis and conclude that the coefficient if x is 0.

It can therefore be concluded that the sample statistic indicates that there is a statistical evidence to support the notion that the x intercept is 0, therefore the demand and the unit price are not related at α = 0.05.

1. Since there is no correlation between the variables the coefficient of determination will be 0
2. The coefficient of correlation for variables which are totally independent of each other is 0
3. From the output the linear equation

     can be derived, using this equation and the value of X at 50000 we obtain    

Question 3

1. A NOVA table

Advise

In this section we conduct a hypothesis test where the null hypothesis indicates that all the group means are equal and the alternate hypothesis is stated as at least one mean is difference.

The p value obtained is 0.00557

When compared to the value of alpha

, we can see that , this falls within the rejection region hence we reject the null hypothesis.

It can therefore be stated that the sample data provides an evidence to conclude that the means of the programs are statistically different.

Allied corporation should be advised that the impact of the four programs on the employee’s productivity have a statistical difference. Being that Program C have the greatest mean productivity with a small variance it should be incorporate in the firm’s program.

Question 4

1. Regression equation

The regression output is displayed below

From the output the equation is obtained as

1. At alpha equals to 0.10 the significance is obtained as 0.0526. since this value is less than alpha, we can conclude that the model is overall Significant.
2. The p value for the competitor’s price is 0.0362, this value is lower than the 0.10 level of significance hence it can be concluded that the price is individually significant in relation to the sales values. On the other hand, the p value for advertising is obtained as 0.9697 which is higher than 0.10. the conclusion is that the adverting is not individually significant to the sales values at 0.1 level of significance.
3. New estimated regression model

From the new model the revised estimated equation is obtained as slope of the model is given by 41.0603, this means that for a unit increase in the price of the competitors products the sales volume of the company’s products goes up by 41.603 units

References

Andrew, G., 2008. Variance, analysis of. The new Palgrave dictionary of economics. 2nd ed. Basingstoke, Hampshire New York: Palgrave Macmillan.

Bailey, R. A., 2008. Design of Comparative Experiments, s.l.: Cambridge University Press.

Klaus, H. & & Oscar, K., 2008). . Design and Analysis of Experiments. I and II ed. s.l.:Wiley.

Scott, J. A., 2012. Illusions in Regression Analysis. International Journal of Forecasting, 28(3), p. 689.

Willem, W., Baets, D. & Luc, B., 2008. ROC analysis in ordinal regression learning. Pattern Recognition Letters, Volume 29, p. 1–9.

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