a)
Random sampling is where each element of a given population has equal chances of being included in the sample since the sampjle is picked arbitrarily. Once the sampling frame is identified, the researcher uses a table of random numbers to select the sample or through computer generated numbers. The main advantage of random sampling is that the same is a representative of the entire population. It also eliminates researcher bias. Besides, it allows for application of inferential statistics. The main disadvantage of random sampling are that it is complex.
b)
It is primary data and not secondary data from the company viewpoint. This is because it is the company that collected the data. Primary data is data that is for the first time by the investigator.
c)
The outlier is the sales value of 2013. This is because it is much higher than the rest of the numbers. While all of the other sales range from 3000 to 4000 units, the sales for 2013 is greater than 6000 units.
d)
i)
The mean price was 19.91 pounds while the median price was 19.6. The mean sales were 3,592.25 and the median sales were 3,288.
ii)
The range for price was 3.2 while that of sales 3355. The variance for price was 1.04 and the standard deviation was 1.02. The variance for sales was 864617.8 and the standard deviation was 929.84.
e)
i)
ii)
iii)
iv)
The slope is -205.54. The negative sign shows a negative relationship. Therefore, the slope means that increasing price by one pound reduces sales by 205.
v)
The intercept means that when the price is zero the sales will be 7,685.94.
f)
An increase in price by 2 pounds will reduce sales by 411.08 An increase in price by one pound reduces sales by 205.54 according to the slope. Therefore, an increase in price by 2 will be:
Reduction = 205.54*2 = 411.08
g)
Sales = 7,685.94 – 205.54*25 = 2,547.48
h)
It will not be appropriate. The prices may not reduce to zero. Besides, at some price no consumer will be willing to buy any longer.
The government should not allow Tata Steel to shut down. Shutting down the company will result in many people losing their jobs. From the data, it can be observed that the company has high sales. Therefore, there must be a number of people who depend directly on the company for the livelihood. Besides, there are those people who are employed indirectly by the company. The company must use other services and goods to operate.
There is also a solution to the problem that faces the company. It is observed that there is a negative relationship between price and sales. That is an increase in price reduces sales. Therefore, the slope means that increasing price by one pound reduces sales by 205. Therefore, the government can help the company by facilitating it to reduce its prices. This can be done by giving the company subsidies for its products. Therefore, the firm unit production cost is lower hence it can supply it at a lower price. Based on the regression equation, the reduction in price will improve revenues and increase the profitability of the company. Consequently, it will be able to continue in operations.
The government can also help the company to acquire superior technology. A superior technology with a higher efficient will reduce the unit production costs. Therefore, the company can be able reduce its prices in the long run in a sustainable manner and maintain profitability. A subsidy can only be applied as a temporary measure since the government cannot continue giving the company money every period.
The explanatory power of a model is measured by the adjusted R-square. It is the percentage of the variations of the dependent variable that is explained by the model. The higher the R-square the higher the explanatory power of the model. In this case, the adjusted R-square is 0.04. Therefore, the model explains very little of the variations in the sales. This implies that there are many other factors which are not being considered by the model. Secondly, ANOVA test for regression show that the F-statistic for regression is 0.53 which translates into a p-value of 0.48. Therefore, the model is not significant at 10 percent significance level. Besides, a t-test for the regression co-efficient gives a t-statistic of 1.37 which translates into a p-value of 0.19. Therefore, the co-efficient of the price is not significant. Therefore, price is not an important determinant of sales.
The government needs to help the company to identify the drivers of sales in the steel market. That way, an appropriate turnaround strategy can be applied. The strategy may need the help of the government or it may be due to small internal issues that the company can solve.
However, it should be appreciated that a linear model may not be the best model to explain the data. Therefore, alternative model specifications should be investigated.
Bibliography
Barbie , E., 2016. The Basics of Social Research. London: Cengage Learning.
Jha, 2012. Quantative Aptud:Statistics For Ca-Cpt. New Delhi: Tata McGraw-Hill Education.
Rubin, A., 2012. Statistics for Evidence-Based Practice and Evaluation. London: Cengage Learning.
