Statistics: correlation between retail online sales and total retail sales - Essay Example

Statistics: correlation between retail online sales and total retail sales To calculate the correlation coefficient for quarterly retail online sales and corresponding total retail sales for the recent few years, we use the formula: Let Xi be total retail sales, and Yi - retail online sales for period i. N is total number of pairs of observations and is equal to total number of periods available, thus N = 19.#xyx*yx*xy*y1787,2125,3354,199,776,020619,702,732,94428,462,2252714,5615,6634,046,558,943510,597,422,72132,069,5693774,6776,1854,791,377,245600,124,454,32938,254,2254768,1397,0095,383,886,251590,037,523,32149,126,0815812,8099,1437,431,512,687660,658,470,48183,594,4496724,7317,8935,720,301,783525,235,022,36162,299,4497802,6627,7946,255,947,628644,266,286,24460,746,4368779,0967,8216,093,309,816606,990,577,21661,168,0419850,26510,7559,144,600,075722,950,570,225115,670,02510738,1859,5497,048,928,565544,917,094,22591,183,40111814,62610,0058,150,333,130663,615,519,876100,100,02512818,06110,7348,781,066,774669,223,799,721115,218,75613859,25013,99912,028,640,750738,310,562,500195,972,00114767,43312,1159,297,450,795588,953,409,489146,773,22515852,76012,71810,845,401,680727,199,617,600161,747,52416867,24213,65111,838,720,542752,108,686,564186,349,80117912,10917,51215,972,852,808831,942,827,881306,670,14418834,71615,51512,950,618,740696,750,800,656240,715,22519919,04115,65414,386,667,814844,636,359,681245,047,716Total15,397,575199,050164,367,952,04612,538,221,738,0352,321,168,318First, we calculate x*y, x*x and y*y for each pair (xi, yi) and fill out the three last column of the table about.

Second, the total for each column is found. Now we have all the numbers necessary to determine the correlation coefficient:R = (19*164,367,952,046 - 15,397,575*199,050)/ (19*12,538,221,738,035 - 15,397,575*15,397,575)*(19*2,321,168,318 - 199,050*199,050) = = 58,103,785,124/ 71,503,127,739 = 0.813The correlation coefficient of 0.813 indicates a strong positive between linear relationship retail online sales and total retail sales variables (X and Y). Therefore, we would expect for the year characterized by the higher level of total retail sales to have also higher level of online retail sales and vice versa.

The relationship between two variables can be described using the linear equation.Correlation is widely used in the everyday business situations when it is necessary to determine the presence and strength of the relationship between two variables. For example, correlation between the advertising expenditures or promotional activities in certain area and the total sales in the corresponding period in that area is of interest for the managers. They want to determine how effective is the advertising/promotion and forecast the sales given increase or decrease in advertising.

However, the correlation values should be treated carefully. It characterizes the strength of the linear relationship; therefore, if the relationship between two given variables is quadratic, logarithmic or exponential, then the correlation coefficient will not adequately reflect how strong the relationship is. Moreover, even the relationship between variables is linear, high positive value of the coefficient does not indicate which of the variables causes the change in the value of another. The situation when both of them are influenced by the third variable and change simultaneously is also possible.

In a business context, a lot of attention should be paid to the economic relationship between variables. For example if the correlation coefficient between sales figures and the amount of calls received by HR department indicates strong positive relationship, it can be a pure coincidence and should not be automatically considered as means to increase sales.