Question

The management of an automobile company tries to find out the effectiveness of staff salary increment on performance of staff. There are more than 1,000 staff in the company and they thought that this would help the company in assessing the staff performance based on salary increment. The company observed the results of 12 employees. The firm has submitted the following data for analysis, Salary pycrement RO 10 all performance 1 15 4 15 17 19 23 27 33 7 9 10 11 45 56 67 46 Required: You are required to calculate alpha and beta coefficient and fit in the regression equation. (1 marks) How much percentage of staff perform below the average ? (1 marks) What is the average increment in the salary? (1 marks) 4 Give your interpretation (1 marks) Sales manager of UIIU tyre company is trying to prepare annual sales budget for the year starting from January. One of the sales person of the company says that more the spends on advertisements, more new customers would come to the UIIU shopping mall. The sales person continued saying that when more new customers come to the mall, company can get more sales and result in more profits. The sales person the company assumes that there is relationship between amount spent on advertisement and the number of new customers to the mall. Number of Mosch ARO February Man 19 77 May Aly 201 7475 R100 9460 1047 7.400 50 57 September Oct Novemba Decem Required: When do we need to calculate correlation? (2 marks) Estimate the relationship between the above two variables using appropriate statistical tool from the above data. (6 marks) Interpret the results thereof.
pls step by step.. and the word limt for interperation (100-125 words)

Answer 1

Q1) a)

Find X · Y and X2 as it was done in the table below. X Y XY X X 1 10 10 13 100 169 1.5 19.5 1.9 15 17 28.5 40.8 2.4 2.7 225 289 361 19 23 51.3 73.6 86.4 3.2 3.2 529 729 3.4 98.6 841 27 29 32 45 3.6 4.1 115.2 184.5 240.8 308.2 1024 2025 3136 56 4.3 4.6 67 4489 Find the sum of every column ΣΧ = 353, ΣΥ = = 35.9, ΣΧΥ = 1257.4, ΣΧ? = 13917 Use the following equations to find a and b: α - ΣΥΣΧ? - ΣΧΣΧΥ η-ΣΧ2 - (Σ Χ)? 35.9 - 13917 – 353 - 1257.4 12 - 13917 – 3532 1.315 και - η-ΣΧΥ - ΣΧ.ΣΥ η-ΣΧ? - (ΣΧ)? 12 - 1257.4 – 353 - 35.9 12 - 13917 – (353)? *0.057 Substitute a and b in regression equation formula y = α + 6.1 y = 1.315 + 0.057 -1

here your alpha is 'a' which is 1.315 and beta is 'b' which is 0.057.

А B с D E 1 2 3 41.67% 4 5 6 7 oc salary increment performance 10 1 performance below average 13 1.5 15 1.9 17 2.4 19 2.7 23 3.2 27 3.2 29 3.4 32 3.6 4.1 56 4.3 67 4.6 29.417 2.992 9 10 11 12 13 14 15 mean 45 16 17

from above 41.67% of staff perfomed below average. You can see red highlighted cells those are the numbers below average=2.992. so percentage = (5/12)*100 = 41.67%

average increment is the mean of increment column which is 29.417.

Interpretation-

as you can see regression equation is

y=1.315+0.057*x so a postive slope coefficient b shows that if we increase the salary of employee their perfromance increases that's pne thing. And quantitatively if we increase the salry by 1% the performace increases by 0.057 % which means let's say someone gets an increment of 30% so his performance is expected to increase by 1.71%.

but don't think that if we increase salary by say 1000% then perfromance will aslo increase by 0.057*1000= 57%

because human capability is limited this model will give results for a short period of time which means for some values of increments around the data.

Q2)

a) correlation is required when we want to have a quick galnce at if a linear relationship exists between two variables and if it exists what is the strength and direction of the relationship.

for eg in the question above the owner of the company is interested in knowing if expenditure on advertisement increases sales or not.

b)

Find X Y , X2 and Y2 as it was done in the table below. Υ.Υ X 7450 Y 89 7921 5230 39 1521 77 5929 6250 5975 52 X Y 663050 203970 481250 310700 560625 850500 1899450 2618315 2704 7475 75 105 Χ. Χ 55502500 27352900 39062500 35700625 55875625 65610000 89302500 114211969 54760000 33640000 73960000 67240000 5625 11025 201 8100 9450 10687 7400 5800 8600 8200 245 40401 60025 7744 3249 88 57 115 651200 330600 989000 1057800 13225 129 16641 Find the sum of every column to get: ΣΧ = 90617, ΣΥ = 1272, ΣΧ.Υ = 10616460, ΣΧ? = 712218619, ΣΥ? = 176010 Use the following formula to work out the correlation coefficient. η-ΣΧΥ – ΣΧ.ΣΥ Y Vn ΣΧ2 - (Σx)”] - [ΣΥ? - (ΣΥ) 12 - 10616460 - 90617 - 1272 ΥΞ 8 0.9427 [12 - 712218619 - 90617?] - [12 - 176010 – 12722]

c)

correlation coefficient always lies between +1 and -1. r = 0.9427 is the correlation coefficient for our question which shows a very strong positive correlation as it is very close to 1 . It means yes there exists a strong linear and direct relationship between amount of expenditure on advertisemnet and number of new customers.
So if we increase advertisement we can expect to see a increase in number of new customers.

I hope this helps you

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