A small Internet company wants to determine how the money they spend on Google A
ID: 3313936 • Letter: A
Question
A small Internet company wants to determine how the money they spend on Google Adwords impacts their monthly revenue. Over 6 consecutive months, they vary the amount they spend on their Adwords campaign (in ) and record the associated revenue (in ) for each month. The data is shown below a) Develop a regresslon cquatlon for predicting monthly revenue based on the amount spent with Adwords. What ls the yntercept? Give your answer to two decimal places. b) What is the proper interpretation of the y-intercept in the regression equations? The y intercept describes the expected decrease in revenue for each additional dollar spent on Adwords. The y intercept describes the expected revenue if the company does not spend any money in a given month on AdWords O The y-intercept describes the expected revenue if the company spends $25 in a given month on Adwords. O The y-intercept describes the expected Incrcase in revenue for cach additional dollar spent on Adwords C) What is the sample correlation between these two variables? Give your answer to two decimal places. d) What is the slope of your regression equation? Glve your answer to two deimal places )Using a 0.1 level of significance, does this regression equation appear to have any value for predicting revenue based on Adwords expenditures? No because there is a significant linear relationship between the two quantities. Yes because there is not a significant linear relationship between the two quantities O Yes because there is a significant linear relationship between the two quantities No because there is not a significant linear relationship between the two quantities.Explanation / Answer
Adwords (x)
Revenue (y)
x^2
y^2
xy
50
540
2500
291600
27000
75
399
5625
159201
29925
100
508
10000
258064
50800
125
576
15625
331776
72000
150
487
22500
237169
73050
175
571
30625
326041
99925
Sum
Sum
Sum
Sum
Sum
675
3081
86875
1603851
352700
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.39
R Square
0.16
Adjusted R Square
-0.06
Standard Error
67.77
Observations
6
ANOVA
df
SS
MS
F
Significance F
Regression
1
3388.13
3388.13
0.74
0.44
Residual
4
18369.37
4592.34
Total
5
21757.50
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
450.89
77.97
5.78
0.00
234.41
667.37
Adwords
0.56
0.65
0.86
0.44
-1.24
2.36
a)
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
= 6*352700-(675*3081)/6*86875-(675^2)
= 0.55657143=> Slope
b0=Ey-b1Ex/n
=3081-(0.55657143)*675/6
=450.8857=> Intercept
b)
The y-intercept describes the expected revenue if the company does not spend any money in a given month on adwords
c)
r (correlation)=n(Exy)-(Ex)(Ey)/sqrt(nEx2-(Ex)2)(nEY2-(Ey)2)
=6(352700)-(675)(3081)/sqrt(6*86875-(675)2)(6*1603851-(3081)2)
=0.3946
d)
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
= 6*352700-(675*3081)/6*86875-(675^2)
= 0.55657143=> Slope
e)
Yes because there is a significant linear relationship between the two quantities
Adwords (x)
Revenue (y)
x^2
y^2
xy
50
540
2500
291600
27000
75
399
5625
159201
29925
100
508
10000
258064
50800
125
576
15625
331776
72000
150
487
22500
237169
73050
175
571
30625
326041
99925
Sum
Sum
Sum
Sum
Sum
675
3081
86875
1603851
352700
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