Linear Regression Analysis

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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.