As a data scientist of a company, you want to analyze the following data collect
ID: 3071779 • Letter: A
Question
As a data scientist of a company, you want to analyze the following data collected by your company which relates the advertising expenditure A in thousands of dollars to total sales S in thousands of dollars. The following table shows this relationship
Using Advertising expenditure (A) as the domain and Total Sales (S) as the range, the data is not a function because the value 18.8 and 19 appear in the domain more than once with a different corresponding value of the range each time.
--Interpret the slope and y-intercept of this equation.
--Express this equation as a function S of A and find its domain.
--Predict the sales if the advertising expenditure is $25000.
Advertising Expenditure (A) Total Sales (S) 18.6 312 18.8 322 18.8 333 18.8 317 19 301 19 320 19.2 305Explanation / Answer
Solution:
intercept of the regression line can be calculated as
a = (summation(y) * summation(X^2) - summation(x)*summation(xy))/n*summation(x^2)-(summation(x))^2
X
Y
XY
X2
Y2
18.6
312
5803.2
345.96
97344
18.8
322
6053.6
353.44
103684
18.8
333
6260.4
353.44
110889
18.8
317
5959.6
353.44
100489
19
301
5719
361
90601
19
320
6080
361
102400
19.2
305
5856
368.64
93025
132.2
2210
41731.8
2496.92
698432
So a = (2210*2496.92)-(132.2*41731.8) / (7*2496.92)-(132.2*132.2) = 780.775
Slope of the line can be calculated as
b = n*summation(XY) - summation(X)*summation(Y)/n*summation(X^2) - (summation(x))^2
b = (7*41731.8) - (132.2*2210) / (7*2496.92)-(132.2*132.2) = -24.625
So the equation is in terms of S and A as follows:
S = 780.775 -24.625*A
From the slope we can say that As advertising expenditure increase by 1 unit than sales will decrease by 24.625unit. and intercept tells that if Expenditure is 0 than sales would be 780.775
If Advertising expenditure = $25,000
than Sales. = 780.775 -24.625*25 = 780.775 - 615.625 = 165.15 or $165000
X
Y
XY
X2
Y2
18.6
312
5803.2
345.96
97344
18.8
322
6053.6
353.44
103684
18.8
333
6260.4
353.44
110889
18.8
317
5959.6
353.44
100489
19
301
5719
361
90601
19
320
6080
361
102400
19.2
305
5856
368.64
93025
132.2
2210
41731.8
2496.92
698432
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