A company randomly samples 48 months of monthly output and monthly total cost data. The sampled data will be used to develop a total cost curve for the company. The company believes that its monthly total cost depends, to a large extent on its monthly output, and hopes that a simple linear regression model will be useful in analyzing how total costs vary as monthly output varies. The company proposes the following model: Total Cost = Fixed Cost + Variable Cost per Unit *Monthly Output. Recall that fixed costs do not vary with the level of monthly output, while the variable cost per unit describes the change in total costs when monthly output changes by one unit. Regression Statistics Standard Error 64.252 Observations 48
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![A company randomly samples 48 months of monthly
output and monthly total cost data. The sampled data will
be used to develop a total cost curve for the company. The
company believes that its monthly total cost depends, to a
large extent on its monthly output, and hopes that a simple
linear regression model will be useful in analyzing how
total costs vary as monthly output varies. The company
proposes the following model: Total Cost = Fixed Cost +
Variable Cost per Unit *Monthly Output. Recall that
fixed costs do not vary with the level of monthly output,
while the variable cost per unit describes the change in
total costs when monthly output changes by one unit.
Regression Statistics
Standard Error| 64.252
Observations
48
ANOVA
df
SS
MS
Regression 1
3097160 3097160
Residual
46
189904
4128
Total
47 3287064
Standard
Error
Coefficients
I Stat
Intercept
38.25
24.28
1.6
Monthly Output
19.69
0.72
27.4
A statistician has been asked by the company to conduct a
statistical test to determine if the overall regression model
is significant. To conduct this test the statistician will
need to compute the appropriate test statistic. The
calculated test statistic that the statistician needs to
conduct this test is
F = = 3097160/189904 =16.3
F = =3097160/4128 = 750.3
Z = Intercept/Monthly Output
а.
b.
с.
38.25/19.69 = 1.94
d.
F = = 3097160/3287064 = 0.9422](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94cdfbf1-be4d-45d3-9fdb-fe2de59b1878%2F772028bb-f328-43e8-8761-7296523d6d9b%2F5re4zyp_processed.jpeg&w=3840&q=75)
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