From the above histogram, it is apparent that the distribution is assymetric and also there is present of skew on the left considering the fact that tail on the left seems longer than the one on the right. As a result, it is apparent that the distribution of preparation time is not normally distributed (Fehr & Grossman, 2013).
The frequency distribution of the marks is indicated below.
From the above histogram, it is apparent that the distribution is assymetric and also there is present of skew on the left considering the fact that tail on the left seems longer than the one on the right. As a result, it is apparent that the distribution of exam marks is not normally distributed (Flick,. 2015).
Mark = 28.984 + 0.5831*Preparation Time
If the preparation time would increase by 1 hour, then the marks would increase by 0.583.
Based on the above, it is appropriate to conlcude that the two variables have a positive relationship owing to the positive sign of the correlation coefficient. Also, this relationship is moderately strong considering that it is greater 0.5 and the theoretical maximum is 1 (Hastie, Tibshirani & Friedman, 2014).
The completed table is shown as follows.
Considering the table above, the relevant information is summarised below.
F statistic = (4710.79/65.10) = 72.336
Based on the above, the p value has come out as 0.00.
As P value < Level of Significance, H0 is rejected but H1 is accepted (Hair et. al., 2015). The conclusion can be drawn that the multiple regression model is statistically significant as there exists atleast one slope coefficient which is non-zero (Flick, 2015).
X1 Slope coefficient: It indicates that a change in father’s height by 1 unit would bring about a corresponding change in the son’s height by 0.48 units and both the changes would be in the same direction.
X2 Slope coefficient: It indicates that a change in mother’s height by 1 unit would bring about a corresponding change in the son’s height by 0.02 units and both the changes would be in the opposite direction.f) The requisite hypotheses to be tested are summarised as follows.
On the basis of the provided regression output, it becomes evident that the X1 variable slope coefficient is significant owing to the fact that corresponding p value amounts to 0.000 and therefore would not exceeds the level of significance. The net result would be rejection of null hypothesis and acceptance of alternative hypothesis. Therefore, it is correct to conclude the son’s height is related to their father’s height.
References
Eriksson, P. & Kovalainen, A. (2015) Quantitative methods in business research. 3rd ed. London: Sage Publications.
Fehr, F. H. & Grossman, G. (2013). An introduction to sets, probability and hypothesis testing. 3rd ed. Ohio: Heath.
Flick, U. (2015) Introducing research methodology: A beginner’s guide to doing a research project. 4th ed. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015) Essentials of business research methods. 2nd ed. New York: Routledge.
Hastie, T., Tibshirani, R. & Friedman, J. (2014) The Elements of Statistical Learning. 4th ed. New York: Springer Publications.
Hillier, F. (2016) Introduction to Operations Research. 6th ed. New York: McGraw Hill Publications.
Lieberman, F. J., Nag, B., Hiller, F.S. & Basu, P. (2013) Introduction To Operations Research. 5th ed. New Delhi: Tata McGraw Hill Publishers.
Medhi, J. (2016) Statistical Methods: An Introductory Text. 4th ed. Sydney: New Age International.
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