Introduction
This report contains the results of regression analysis for four variables captured in the Springdale community shopping survey. The analysis established that there was significant linear relationship between attitude towards Springdale and ease of return/exchange of goods. However, there was no significant linear relationship between the attitude towards Springdale and a lot of bargain price. On the other hand, it was found that there was significant linear relationship between attitude towards West Mall and a lot of bargain sales. On the contrary, there was no significant linear relationship between attitude towards West Mall and ease of return/exchange of goods.
- Regression Analysis
Correlation between easy to return/exchange goods and attitude towards Springdale
Summary of Excel Output Results
The regression equation
Y = 0.172X + 2.920
Where 0.712 is the gradient of the line and 2.920 is the y-intercept
The above regression line shows that there is a positive linear relationship between ease with which goods are returned or exchanged and the attitude towards Springdale. The attitude increases with increase in the ease with which goods are exchanged.
The Excel analysis shows that the correlation coefficient between ease of return/exchange of goods and attitude towards Springdale is 0.290. This coefficient falls between 0.1 and 0.3. Consequently, it can be concluded that the correlation between the eases of return /exchange of goods and attitude towards Springdale is modest. The coefficient of determination based on the excel result output is 0.0841. This means that 8.41% of the changes in attitude towards Springdale can be attributed to ease of return/exchange of goods.
Hypothesis testing
Null Hypothesis: H0: ρ = 0
There is no linear relationshipAlternative hypothesis: H1: ρ ≠ 0
The p-value based on Excel result output is 0.00031729. This is less than the significance level (0.05). Therefore, the null hypothesis is rejected. There is significant linear relationship between the ease of return/exchange of goods and attitude towards Springdale.
Correlation between a lot of bargain sales and attitude towards Springdale
Summary of Excel Output Results
The regression equation
Y = 0.023X + 3.694
Where 0.023 is the gradient of the line and 3.694 is the y-intercept
The above regression line shows that there is a positive linear relationship between a lot of bargain sales and the attitude towards Springdale. The attitude increases with increase in the magnitude of bargain sales.
The Excel analysis shows that the correlation coefficient between a lot of bargain sales and attitude towards Springdale is 0.0361. This coefficient is less than 0.1. Consequently, it can be concluded that the correlation between a lot of bargain sales and attitude towards Springdale is weak. The coefficient of determination based on the excel result output is 0.0013. This means that 0.13% of the changes in attitude towards Springdale can be attributed to a lot of bargain sales.
Hypothesis testing
Null Hypothesis: H0: ρ = 0
There is no linear relationshipAlternative hypothesis: H1: ρ ≠ 0
The p-value based on Excel result output is 0.660154. This is greater than the significance level (0.05). Therefore, the null hypothesis is upheld. There is no significant linear relationship between a lot of bargain sales and attitude towards Springdale.
Correlation between return/exchange of goods and attitude towards West Mall
Summary of Excel Output Results
The regression equation
Y = 0.035X + 3.469
Where 0.035 is the gradient of the line and 3.469 is the y-intercept
The above regression line shows that there is a positive linear relationship between ease with which goods are returned or exchanged and the attitude towards West Mall. The attitude increases with increase in the ease with which goods are exchanged.
The Excel analysis shows that the correlation coefficient between ease of return/exchange of goods and attitude towards West Mall is 0.053. This coefficient is less than 0.1. Consequently, it can be concluded that the correlation between the eases of return /exchange of goods and attitude towards West Mall is weak. The coefficient of determination based on the excel result output is 0.0028. This means that 0.28% of the changes in attitude towards West Mall can be attributed to ease of return/exchange of goods.
Hypothesis testing
Null Hypothesis: H0: ρ = 0
There is no linear relationshipAlternative hypothesis: H1: ρ ≠ 0
The p-value based on Excel result output is 0.51780475. This is greater than the significance level (0.05). Therefore, the null hypothesis is upheld. There is no significant linear relationship between the ease of return/exchange of goods and attitude towards West Mall.
Correlation between a lot of bargain sales and attitude towards West Mall
Summary of Excel Output Results
The regression equation
Y = 0.093X + 2.800
Where 0.093 is the gradient of the line and 2.800 is the y-intercept
The above regression line shows that there is a positive linear relationship between a lot of bargain sales and the attitude towards West Mall. The attitude increases with increase in the magnitude of bargain sales.
The Excel analysis shows that the correlation coefficient between a lot of bargain sales and attitude towards Springdale is 0.365. This coefficient falls between 0.3 and 0.5. Consequently, it can be concluded that the correlation between a lot of bargain sales and attitude towards West Mall is moderate. The coefficient of determination based on the excel result output is 0.0177. This means that 1.77% of the changes in attitude towards West Mall can be attributed to a lot of bargain sales.
Hypothesis testing
Null Hypothesis: H0: ρ = 0
There is no linear relationshipAlternative hypothesis: H1: ρ ≠ 0
The p-value based on Excel result output is 0.105027427. This is less than the significance level (0.05). Therefore, the null hypothesis is rejected. There is significant linear relationship between a lot of bargain sales and attitude towards West Mall.
- Testing assumptions
Correlation between easy to return/exchange goods and attitude towards Springdale
The residual points are almost equally spread above and below the horizontal line. Consequently, the data has linearity.
The shape of the above histogram is almost similar to the normal distribution curve. The frequency of the residual reduces as one move further away from the mode. Therefore the data has normality.
The plots are almost evenly distributed on each side of the trend line. Consequently the data has normality.
Correlation between a lot of bargain sales and attitude towards Springdale
The residual points are to a greater degree not evenly distributed above and below the horizontal line. Consequently, the data lacks linearity.
The shape of the above histogram above does not resemble the shape of the normal distribution curve. Consequently, the data lacks normality.
The residual points are almost equally spread above and below the horizontal line. Consequently, the data has linearity.
Correlation between ease of return/exchange of goods and attitude towards West Mall
The residual plots are almost evenly distributed above and below the horizontal line. Consequently, the data has linearity.
The data lacks normality because the shape of the histogram is not similar to the normal distribution curve.
The above graph shows that the data on attitude towards West Mall has normality. The plots are almost evenly distributed on either side of trend line.
Correlation between a lot of bargain sales and attitude towards West Mall
The residual plots are almost evenly distributed along the horizontal line. Consequently, the data has linearity.
The histogram above shows that the data lacks normality.
Conclusion
The Springdale should introduce a lot of bargain sell to attract more shoppers and increase their attitude towards the mall. On the other hand, West Mall should make it possible for customers to return/exchange goods freely and quick in order to retain its customers and improve their attitude towards the mall.
