APPLIED MANAGERIAL STATISTICS

Running head: APPLIED MANAGERIAL STATISTICS 1
Maths 534: Applied Managerial Statistics
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APPLIED MANAGERIAL STATISTICS 2
Applied Managerial Statistics
Step 1
The scatter plot for sales (Y) against Calls (X) is shown below. The variable sales represent the
dependent variable hence placed on the vertical axis while calls represent the independent
variable and is place on the horizontal axis (Holmes, Illowsky & Dean, 2019)
The scatter plot indicates that there is a positive linear relationship between sales and calls.
Therefore, an increase in the number of calls made in a week would result to an increase in the
number of sales made during the week.
Step 2
The equation of the “best fit” line that explains the relationship between the independent and the
dependent variable is:
Y =0.1278 x +23.141
Where Y is the dependent variable (sales) and x is the independent variable (calls). In terms of
the variables the equation can be written as:
Sales ( Y ) =0.1278 Calls( X )+23.141

APPLIED MANAGERIAL STATISTICS 3
The coefficient of calls or the slope of the regression line shows that the independent variable
(calls) impact the dependent variable (sales) by a magnitude of 0.1278 while the intercept shows
the value of sales would be 23.141 given that no calls were made.
Step 3
The coefficient of correlation can be determined from the scatter plot as:
R= √ R2
R= √ 0.1095
R=0.3309
It can also be determined using the correlation matrix below.
Correlation matrix
Calls (X1) Sales (Y)
Calls (X1) 1
Sales (Y) 0.330919 1
The coefficient of correlation (0.3309) show that the amount of relationship between the
independent and dependent variable that can be explained by the data is equal to 33.09% (Bruce,
2015)
Step 4
The coefficient of determination is the R-squared value shown in the scatter plot. It is equivalent
to:
R−squared=0.1095
The coefficient of determination (0.1095) shows that the amount of variability in the dependent
variable that can be explained by the independent variable is equivalent to 10.95% (Levie, 2012)
Step 5
We need to test the utility of the regression equation. The null and the alternative hypothesis can
mathematically be expressed as: