Hi6007 Group Assignment Answers Assessment Answers

Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.

Construct a histogram showing the percent frequency distribution of the furnitureorder values in the sample. Comment on the shape of the distribution. (3 marks)

Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?

Determine whether or not demand and unit price are related. Use α = 0.05.

Compute the coefficient of determination and fully interpret its meaning. Be very specific.

Compute the coefficient of correlation and explain the relationship between demand and unit price.

Answer:

Question 1

The above graph has a shape which would be termed asymmetric owing to the right tail being lenghtier than the left tail which would not occur in a symmetrically shaped graph (Flick, 2015).

• The shape of the above graph would impact the choice of the central tendency measure. Here, the non-symmetric shape provides indication that mean would not be suitable since it could show a higher value of mean under the influence of some high values called as outliers (Taylor &Cihon, 2004). Thereby, preferred central tendency measure would be median since the abnormal values do not impact median (Hillier, 2016).

Question 2

ANOVA

• Hypothesis Testing

In context of slope coefficient of X, test statistic is -8.617 yielding a p value of 0.00. In line with the p value approach, the comparison of the computed p value with 5% α provides requisite evidence for null hypothesis rejection (Lind, Marchal & Wathen, 2012). Thereby, the financial conclusion is that slope coefficient is significant and so is the relation between price and demand (Eriksson and Kovalainen, 2015).

• Coefficient of determination (R square)

The implication of the above value is that 61.71% of dependent variable movements are explained by parallel movements in the independent variable ( Hastie, Tibshirani & Friedman, 2011). Thus, price cannot explain 38.29% of the movements highlighted in the unit demand variable (Flick, 2015).

• Correlation coefficient (R)

The above correlation values would imply that a strong inverse relationship exists between unit demand and price which is not surprising (Hillier, 2016).

Question 3

Degree of freedom (Medhi, 2001) 

Hypothesis testing

In context of ANOVA output, test statistic (F) is 25.85 yielding a p value of 0.00. In line with the p value approach, the comparison of the computed p value with 5% α provides requisite evidence for null hypothesis rejection (Fehr & Grossman, 2003). Thereby, the financial conclusion is that it would be incorrect to conclude that the mean of the given three populations is the same (Flick, 2015).

Question 4 

• Regression output

Equation

• Data has been collected for 7 days.

In context of ANOVA output, test statistic (F) is 80.118 yielding a p value of 0.00. In line with the p value approach, the comparison of the computed p value with 5% α provides requisite evidence for null hypothesis rejection (Harmon, 2011). Thereby, the financial conclusion is that it would be correct to conclude that the linear multiple regression is indeed significant since all slope coefficients are not zero (Hillier, 2016)

• Slope coefficient of variable x1 is significant or not.

In context of slope coefficient of X1, test statistic is 1.078 yielding a p value of 0.206. In line with the p value approach, the comparison of the computed p value with 5% α does not provide requisite evidence for null hypothesis rejection. Thereby, β_X1 is insignificant (Eriksson and Kovalainen, 2015).

• Slope coefficient of variable x1 is significant or not.

In context of slope coefficient of X2, test statistic is 12.23 yielding a p value of 0.00. In line with the p value approach, the comparison of the computed p value with 5% α does provide requisite evidence for null hypothesis rejection. Thereby, β_X2 is significant (Flick, 2015).

• The advertising slope coefficient is representative of the higher daily sale of 0.4733 which can be enabled if one extra advertising spot is used. Further, the decline in advertising spot would lead to corresponding decline in daily mobile sale by 0.4733  (Hillier, 2016).

• Regression equation would be taken into account to find the daily number of phone sold with price of $20,000 and 10 advertising spots (Eriksson & Kovalainen, 2015).

References

Eriksson, P. & Kovalainen, A. (2015) Quantitative methods in business research 3rd ed. London:  Sage Publications.  

Fehr, F. H., & Grossman, G. (2003). An introduction to sets, probability and hypothesis testing (3^rd ed.). Ohio: Heath.

Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research project. 4th ed. New York: Sage Publications.

Harmon, M. (2011). Hypothesis Testing in Excel - The Excel Statistical Master (7^th ed.). Florida: Mark Harmon.

Hastie, T., Tibshirani, R. & Friedman, J. (2011). The Elements of Statistical Learning (4^th ed.). New York: Springer Publications.

Hillier, F. (2016) Introduction to Operations Research 6th ed. New York: McGraw Hill Publications.

Lind, A.D., Marchal, G.W. & Wathen, A.S. (2012). Statistical Techniques in Business and Economics (15^th ed.). New York : McGraw-Hill/Irwin.

Medhi, J. (2001). Statistical Methods: An Introductory Text (4^th ed.). Sydney: New Age International.

Shi, Z. N. & Tao, J. (2008). Statistical Hypothesis Testing: Theory and Methods (6^th ed.). London: World Scientific.

Taylor, K. J. & Cihon, C. (2004). Statistical Techniques for Data Analysis (2^nd ed.). Melbourne: CRC Press.