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Variables & Their Level Of Relationship With Profit Using Multiple Linear Regression (MLR)

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Abstract

The purpose of this paper is to analyze different variables and their level of relationship with profit using multiple linear regression (MLR) method. After a short logical discourse of the framework, the usage of polynomial terms and the way to make the MLR model will be illuminated. Expound on utilization of MLR method using Microsoft EXCEL will be discussed. A brief conclusion on findings of the model will be demonstrated. The best model was found to be Y = -10.170 + 0.027 XFoodSales + 0.097 XNonfoodSales + 0.524 XStoresize + Ei and a variation of 98% in Y(Profit) was explained with a significant P-value of 0.000007.

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Introduction

For any business firm, profitability is an outcome of the interchange between ecological variables and inward factors. It has been claimed by numerous financial scientists that budgetary use is the important factor among alternate factors that can influence the company’s profitability. Non-food sales play an important role in contribution to profit of a supermarket along with food sales and store size. As multi-outlet shopping has expanded, grocery stores have lost a portion of their non-food piece of the pie to other retail channels. Consumers are more into organic and natural products these days. Offering natural and organic items within the store’s non-food divisions, gives another chance to increase in non-food sales and classification execution. Substantial stores energize acquiring of more sustenance in a solitary visit, and in bigger bundles. Also, they give more prominent item decision at low prices and enable more noteworthy introduction to foods of numerous kinds. These qualities may promote buying and utilization. In this paper we discuss on how food, non-food and store size affect profits of a supermarket using multiple regression method. As for case study, we have taken ten supermarkets’ historical data.

Methodology

Regression analysis is one of the vital techniques in business insights. Regression technique examines the connection amongst dependent and independent variables. OLS (Ordinary Least Square) strategy is used to assess the obscure parameters that influences subordinate variable for this paper. We use excel to conduct multiple regression analysis in this paper. Below, is the method and model used in this paper. Multiple regression: In linear regression analysis, we can incorporate more parameters with an end goal to discover factors that better anticipate result. This investigation is known as multiple linear regression analysis. Y = Profit as dependent variable, XFoodSales = Food sales as independent variable, XNonFoodSales= Non-food sales as independent variable, XStoresize= Store size as independent variable, β0 = Intercept, βFoodSales= slope of the straight line characterizing the model, βNonFoodSales= slope of the straight line characterizing the model, βStoresize= slope of the straight line characterizing the model and Ei = Error. Model = Y= β0 + βFoodSalesXFoodSales + βNonfoodSalesXNonfoodSales + βStoresizeXStoresize +Ei

We have achieved below equation from excel results obtained Y = -10.170 + 0.027 XFoodSales + 0.097 XNonfoodSales + 0.524 XStoresize + Ei Standard error T-Stat P value Coefficients Intercept 3.473128593 -2.928265696 0.026346428 -10.17024332 Food Sales 0.012040996 2.245504802 0.065846812 0.027038115 Non-food Sales 0.030147122 3.219290578 0.018153389 0.097052345 Store size 0.059158249 8.869011174 0.000114333 0.524675168 F-Value for the equation was found to be 130.0599363 The coefficient βFoodSales or βNonfoodSales or βStoresize confers by what aggregate Y would increase if the coherent variable XFoodSales or XNonfoodSales or XStoresize was increased by one unit while the diverse components were kept consistent and this may not be valid for every condition.

Empirical-Results

To give an itemized depiction of the calculations utilized for numerical and graphical outlines of variables, we have selected a small sample size (n) of 10 observations. Below, is the table for mean median and range of all the variables used in this paper FoodSales non-Food Sales Store Size Profit Mean 227 68.6 31.4 19.1 Median 199 76.5 30 18.5 Range 320 67 44 28 Multiple Regression for Food sales, Non-food sales and Store size: Multiple R/ Correlation coefficient R Square/ Coefficient of determination Adjusted R Square Standard Error Observations 0.992398792 0.984855361 0.977283042 1.249867779 10

The Multiple R/Correlation coefficient demonstrates the direct reliance of all the three factors which is 99%. The R Squared/Coefficient of determination shows that 98.48% variance in Y can be clarified by XFoodSales , XNonfoodSales and XStoresize. In this model, R squared is almost near to 1.0 which demonstrates that there is direct connection between the factors and the relationship is linear. Standard Error is the measure of accuracy in this model which is 1.25 for 10 observations.

Skewness: skewness is a measure of symmetry. On the off chance that the skewness of a data set is zero, at that point it is symmetric. If the value is negative, at that point the conveyance is skewed towards left and If the skew is certain then the dispersion is towards right. Statistic Food Sales Non-Food Sales Store size Profit Skewness 0.81261899 -0.451890875 0.383001 0.410959 Kurtosis 0.7380151 -1.48155448 -0.23304 0.292093

Here, Food sales moderately positive skew because it lies between 0.5 and 1. Non-food sales is symmetrical as the skew lies between -0.5 and+-0.5. Whereas store size and profit are also symmetrical because they lie between 0 and +0.5

Kurtosis: Kurtosis is a measure of sharpness of a peak of a distribution curve. If the value is greater than 3 it is leptokurtic, lesser than 3 is platykurtic (flat shape) and equals to 3 is mesokurtic (same shape as normal distribution curve). From the above kurtosis table, the kurtosis of the food sales is greater than 0 indicating a heavier tails (leptokurtic). Non-food sales is less than 0 indicating lighter tails (platykurtic). Store size is less than 0 indicating lighter tails and profit is greater than zero indicating heavier tails.

Hypothesis test

H0: βFoodSales=βNonFoodSales= βstoreSize =β0 = 0 (Food sales, non-food sales and storesize does not affect the profit)

H1: βFoodSales≠ βNonFoodSales≠ βstoreSize ≠ β0 ≠ 0 (Food sales, non-food sales and storesize do affect the profit)

F Test: We may reject the null hypothesis if computed F value is greater than the critical value. Here, α = 0.05 because the confidence interval was set at 95%. If α = 0.05, K-1 = 3 and n-k = 6, the critical value of F (0.05, 3,6) = 4.76. Conclusion: As the computed F value 130.0599 > Critical value F (0.05, 3,6) which is 4.76 indicating that we may reject the null hypothesis. This concludes atleast on of the three independent variables is a significant predictor of supermarket profits.

T Test for (XFoodSales): At α = 0.05, if the computed T value is greater than the critical value, we may reject the null stating food sales contributed in predicting profit. Here, α/2 = 0.05/2 = 0.025 because it is a two tailed test. If n-k = 6, T (0.05/2, 6) = 2.96. Conclusion: As the computed T value for food sales 2.245 < T (0.05/2, 6) = 2.96, we do not reject the null concluding food sales does not contribute useful information in predicting profits.

T Test for (XNonfoodSales): At α = 0.05, if the computed T value is greater than the critical value, we may reject the null stating non-food sales contributed in predicting profit. Here, α/2 = 0.05/2 = 0.025 because it is a two tailed test. If n-k = 6, T (0.05/2, 6) = 2.96. Conclusion: As the computed T value for food sales 3.22 > T (0.05/2, 6) = 2.96, we reject the null and concludes non-food sales contribute useful information in predicting profits.

T Test for (XStoresize): At α = 0.05, if the computed T value is greater than the critical value, we may reject the null stating store size contributed in predicting profit. Here, α/2 = 0.05/2 = 0.025 because it is a two tailed test. If n-k = 6, T (0.05/2, 6) = 2.96. Conclusion: As the computed T value for food sales 8.87 > T (0.05/2, 6) = 2.96, we reject the null and concludes store size is an excellent predictor of profits. P- Value: If α is > P-value, we may reject the null. Here, α = 0.05 > P-value (0.000007) hence, we reject the null hypothesis.

Results and Discussion:

As per the model, 98.48% of variation in the y could be explained by the independent factors. Food sales was not removed from the test to maintain accuracy of Y. The P-value 0.000007 is significant because it is less than α = 0.05. From our results it was confirmed that store size and non-food sales have great impact on profit. Supermarkets should concentrate more on non-food and store sizes to achieve profits. Bigger store size encourages consumers to buy more. Where as non-food items when given at temporary low prices attracts the crowd into the store.

Conclusion

Our research was mainly focused on supermarket sales and profits, to 10 observations. Our findings support the importance of non-food sector and store size in the prediction of profits. Non-food sales and store size are excellent predictors of profits of the supermarket. Regarding the limitation, our paper discusses about limited number of supermarkets.

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