Question

A professor aims to explore and determine the importance of spending more time in understanding the data behaviour and run the exploratory data analysis. He claims that the longer the time (in hours per day) student’s spent on both aspects will produce more excellence output in terms of writings and results (in average pages). Therefore, a random sample of 11 degree students were chosen and their output produced items were recorded as in Table 1. Draw the conclusion from the result of the appropriate analysis.

Table 1

Time (hours per week)	4	3	5	7	8	9	7	6	5	9	10
Output	7	8	9	13	14	15	11	10	11	15	16

Answer 1

Lets first plot the graph to get a better visual understanding of the data. The plot is shown below.

We have also added a logartithmic trendline here. Lets see what these tell us.

First, lets see why we have used the log regression line and not linear. This is because the relationship between time spent and output is not only not linear, but also changes direction couple of times. If we had used a linear regression, we would not have been able to capture this change and its effect.

A log regression is used when the relationship is fast at first and then changes. We can see that initially the output increases rapidly with increase in time spent but then goes negative and then come back.

As we can see from the equation shown in the cart, the relationshio between output (y) and of time spent (x) can be predicted by

output=3.0409Ln(time spent)+6.8889

What its saying is that, on an average, the output will rise rapidly at first with increase in time spent, but the rate of increase will slow down as we spend more time. Effectively, it shows diminishing returns.