The table below gives the number of parking tickets received in one semester and

Question

The table below gives the number of parking tickets received in one semester and the GPA for five randomly selected college students who drive to campus. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the GPA of a college student who drives to campus based on the number of parking tickets they receive in one semester. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Table

Step 4 of 6:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆy^.

Number of Tickets 00 22 55 66 77 GPA 3.73.7 3.43.4 3.13.1 2.32.3 1.81.8

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: GPA
Independent Variable: Number of tickets
GPA = 3.86 - 0.25 Number of tickets
Sample size: 5
R (correlation coefficient) = -0.92343312
R-sq = 0.85272873
Estimate of error standard deviation: 0.34976182

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Change in dependent variable for a unit increase in x

= Slope

= -0.25

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 3.86 0.28641804 0 3 13.476805 0.0009 Slope -0.25 0.059983658 0 3 -4.1678018 0.0251

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