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Linear Regression Analysis
Student’s Name
Institution Affiliation
Course Name and Code
Professor’s Name
Date
Linear Regression Analysis
The type of relationship.
Based on the scatter plot plotted, there exists a strong positive linear relationship between rate of service and worker hours.
Develop a linear regression model to explain the variation in the service rating.
The linear regression model is as follows:
????̂=66.7111+1.0617????
The coefficient of determination (R²) =83.81%
Therefore, 83.81% of the variation in the rate of service can be explained by the variation in the worker hours, while the other variation could be explained by other factors outside the model.
Describe the model, showing the results of the pertinent hypothesis tests, using a significance level of 0.10.
Hypothesis
Here, we test whether there exists a significant relationship between rate of service and Worker hours. Thus,
H0: ρ=0
H1: ρ≠0
Test statistic
From the regression output;
The correlation coefficient (r)= 0.9155
t=7.8828
Degrees of freedom
n-2=14-2=12.
P_value
Using the excel function, “=2*(1-T.DIST(7.8828, 12, TRUE))”
P_value=4.37173E-06=0.0000
α=0.10
P_value (0.0000) < α (0.10)
Therefore, since P_value < α we reject the null hypothesis and conclude that there is enough evidence to support that there is a significant relationship between the rate of service and worker hours at the significance level of 0.10.
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