Correlation and Regression in Statistics - Paper Example

One of the most important tests in statistics is the correlation test. It is used in checking the association and dependability that exists between two quantitative variables. The underlying assumption is that the association exhibited is linear such that any change in one of the variables directly affects a unit change in the other. Another technique is regression (Sharma, 2005). It usually involves a process that yields an estimate of the best line of fit that summarizes the level of association (Kelly, 2007). The degree of association is determined by the coefficient correlation which can either be positive (+v) or negative (-v). The scale of correlation runs from -1 0 +1 (Sharma, 2005). This study examines the correlation and regression level between two variables, that is, the size of the bill and customer satisfaction based on data collected on customers.

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

Order now

Analysis

Correlation Analysis

The analysis under this part attempts to establish whether there is a link between size of the bill and customer satisfaction. The following is the hypothesis test that will help achieve this objective:

Null hypothesis (H0): Customer satisfaction is directly related to the size of the bill

Alternative hypothesis (HA): Customer satisfaction is not directly related to the size of the bill.

Table 1 below exhibits the output of correlation analysis

Table 1: Correlation Analysis

Customer Service Rating Total Bill

Customer Service Rating 1

Total Bill 0.6209 1

From table 1 above, the correlation coefficient between customer service rating and the total bill is 0.6209. This is a strongly positive correlation. Based on this output, it is worth indicating that there is direct relationship between customer service rating and the size of the bill offered at the restaurant (Kelly, 2007). Hence, we fail to reject null hypothesis as established above.

Regression Analysis

Based on a similar hypothesis established above, regression is used in this case to help establish the best line of fit that describe the relationship between customer service rating and the size of the bill (Kelly, 2007). The same data is used and the results are displayed under table 2.

Table 2: Regression Analysis

R Squared = 0.3855 38.55%, Confidence Interval, (CI) = 95%

Coefficients Standard Error t Stat P-value

Intercept 49.96 2.12 23.60 0.00

Total Bill 0.33 0.04 7.84 0.00

From the regression output, it is possible to establish a regression model that defines the line of best fit as follows:

Customer Service Rating = 0.33 (Total Bill) + 49.96

Based on the equation, it can be noted that holding all other factors constant, the customer service rating will be equivalent to 49.96. However, the rating increases by 0.33 units following a unit increase in the size of the bill. This displays a direct relationship that have been identified by correlation. Based on R squared value, it is shown that size of the bill only affects 38.55% of all the changes in the customer service rating. The remaining 41.45% are described by factors not included in the model. Besides, it can established that size of the bill is statistically significant at 5% significant level as indicated by p-value of 0.00 that lies within this range.

Conclusion

Evidently, the analysis output shows that there is a direct link between customer satisfaction and the size of the bill. It is reported that, an increase in the size of the bill increases the customer service rating, hence satisfaction. This is reported through a positive correlation coefficient which is also confirmed by regression analysis.

References

Kelly, B. (2007). Statistics with the TI-84 Plus & TI-84 Plus SE. Burlington, Ont: Brendan Kelly Pub.

Sharma, A. (2005). Text book of correlation and regression. New Delhi: Discovery Publishing House.