We have been assigned to determine how the total weeklyproduction cost for Widgetco depends on the number ofwidgets produced during the week. The following modelhas been proposed:Y b0 b1X b2X2 b3X3 where X number of widgets produced during the weekand Y total production cost for the week. For 15 weeksof data, we found that SSR 215,475 and SST 229,228.For this model, we obtain the following estimated regressionequation (t-statistics for each coefficient are in parentheses):yˆ 29.7 19.8X 0.39X2 0.005X3(0.78) (0.62) (1.25)a For a 0.10, test H0: bi 0 against Ha: bi 0(i 1, 2, 3).b Determine R2 for this model. How can the high R2value be reconciled with the answer to part (a)?
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.
We have been assigned to determine how the total weekly
production cost for Widgetco depends on the number of
widgets produced during the week. The following model
has been proposed:
Y b0 b1X b2X2 b3X3
where X number of widgets produced during the week
and Y total production cost for the week. For 15 weeks
of data, we found that SSR 215,475 and SST 229,228.
For this model, we obtain the following estimated regression
equation (t-statistics for each coefficient are in parentheses):
yˆ 29.7 19.8X 0.39X2 0.005X3
(0.78) (0.62) (1.25)
a For a 0.10, test H0: bi 0 against Ha: bi 0
(i 1, 2, 3).
b Determine R2 for this model. How can the high R2
value be reconciled with the answer to part (a)?
Given that,
Dependent variable (y) = total production cost
There are three independent variables.
k = 3
Sample size (n) = 15
SSR = 215,475
SST = 229,228
The regression equation is,
t (x) = 0.78
t (x2) = 0.62
t(x3) = 1.25
Level of significance () = 0.10
Test the given hypothesis using F-test.
To compute the value of R2.
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