You manage a staff of 10 sales professionals for a distributor of IT products an
ID: 3207170 • Letter: Y
Question
You manage a staff of 10 sales professionals for a distributor of IT products and services. Over the past 6 months you have been tracking the number of client visits each sales person makes per week and have created a summary measure for average number of visits per week. Paired to this you have tallied sales in the first six months of the year for each sales person. As you look at the numbers, you postulate that there might be a relationship between the two variables and you formally want to investigate the possibility. The Data is listed below:
SalesPerson
Client Visits Per week
YTD Sales
Caleb
7.85
46.54
Josiah
14.87
67.21
Eileen
10.68
70.62
Chanda
10.1
51.03
Rodderick
13.83
74.5
Dimiya
12.73
60.79
Leena
6.84
57.08
Addison
7.72
38.51
Shah
4.06
42.02
John
1.71
23.07
Could someone please help me figure out how to solve these step by step?
Q1 – Which variable (Avg # Visits or YTD Sales) would you classify as the Independent (X) variable and which as the dependant (Y) variable? Why?
Q2 – Create an Appropriate Scatterplot of these two variables.
Q3 – Estimate the slope and intercept for a linear Ordinary Least Squares regression line using the data for the two variables provided.
Q4 – What is the RSquared for the model you estimated?
Q5 – What is the Standard error of the estimate (Se) for your model?
SalesPerson
Client Visits Per week
YTD Sales
Caleb
7.85
46.54
Josiah
14.87
67.21
Eileen
10.68
70.62
Chanda
10.1
51.03
Rodderick
13.83
74.5
Dimiya
12.73
60.79
Leena
6.84
57.08
Addison
7.72
38.51
Shah
4.06
42.02
John
1.71
23.07
Explanation / Answer
Q1) avg#visits is the independent(X) variable as that does not depend on the sales. Instead it is the YTD sales that depends on the number of visits made by the sales professionals. Hence YTD sales is the dependent(Y) variable.
Q2) Type in the following commands in R console:-
>x<-c(7.85, 14.87, 10.68, 10.1, 13.83, 12.73, 6.84, 7.72, 4.06, 1.71)
>y<-c(46.54, 67.21, 70.62, 51.03, 74.5, 60.79, 57.08, 38.51, 42.02, 23.07)
>plot(y~x)
and then the scatter plot is displayed. The plot shows a positive linear relationship.
Q3) The slope amd intercept can also be calculated using R. First create a data frame called "data" consisting of x(avg#visits) and y(YTD sales) values as follows:-
> data<-data.frame(x, y)
Now form the linear model called "fitted.model" by using the following commands:-
> fitted.model <- lm(y~x, data=data)
>print(fitted.model)
now we get the intercept value as 23.176 and the slope as 3.315
Q4) To find the correlation use the simple command :-
>cor(x,y)
and it will show an output of 0.8721815. Now square this to get the rsquared value, which is 0.760700569.
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