STA 101 : Statistics

2. Statistical analysis of has shown a strong negative correlation between skiing accidents and consumption of ice-cream in a data set of various countries in 2017. Are these statistical findings a proof of causal relationship between these two variables? Explain.

‘The actual account balance’ = 7.183895565 + 1.024805453 * ‘The computer generated balance’ (Neter et al. 1996).

‘The actual account balance’ = 7.183895565 + 1.024805453 * ‘The computer generated balance’.

Or, ‘The actual account balance’ = 7.183895565 + 1.024805453 * 100

Or, ‘The actual account balance’ = 7.183895565 + 102.4805453

Or, ‘The actual account balance’ = 109.6644409

‘The actual account balance’ = -4.84305113 + 0.959108326 * ‘The computer generated balance’.

‘The actual account balance’ = 19.2108423 + 1.09050258 * ‘The computer generated balance’.

When, the computer generated balance of Mr. Oliver Buxton is accounted as 100, then the upper and lower 95% confidence intervals of actual balances are respectively- 128.2611 and 91.06778.

That means, it is 95% probable that actual account balance of Mr. Oliver Buxton ranges in the interval (91.06778, 128.2611).

170.98897 (Upper 95% confidence interval of the average of estimated actual account balance).

128.64739 (Lower 95% confidence interval of the average of estimated actual account balance).

It indicates that there exists 95% probability that the average actual account balance of all the samples lie in the interval of (128.64739 and 170.98897).

Table 2: Table of 95% confidence intervals of average of actual account balance

Alternate 1.d)

The average account balance = 149.8182.

The standrad account balance = 128.2785

95% confidence interval of account balance = 75.80773

The upper and lower 95% confidence limits of the average of account balance are = [74.01046, 225.6259].

2. A statistical analysis shows that a strong negative correlation exists between ‘consumption of ice-cream’ and ‘skiing accidents’ for the analysis of data set of various countries in 2017. However, theses two fcators do not have any ‘cause and effect’ relationship. These two factors are absolutely independent to each other (Box 1966). Therefore, such type of correlation is actually the ‘Non-sense correlation’.

It is the term used to describe a circumstances where two variables are correlated without being causalty associated to each other. Seldom, a third variable could be found out to link a association between two variables. For example, the year wise consumption of food-grain in Europe and life-expecatncy of people of Africa could be highly and positively correlated. Also, the use of solar energy and growth of Malaria in Asian countries could be highly and negatively correlated. However, there exists no significant and explanatory association or ‘cause and effcet’ relation between the pairs of variables. Hence, these cause non-sense correlation.   

References:

Box, G.E., 1966. Use and abuse of regression. Technometrics, 8(4), pp.625-629.

Neter, J., Kutner, M.H., Nachtsheim, C.J. and Wasserman, W., 1996. Applied linear statistical models (Vol. 4, p. 318). Chicago: Irwin.