Question

An automobile insurance company collected 24 months of data to develop a regression model to predict collision claims as a function of the percentage of drivers under age 30 and average temperature. Use the data in the table below to perform the analysis.

a) Describe the relationships between the independent and dependent variables suggested by the scatterplots.
b) Write the equation for this multiple regression model.
c) Formally test the global usefulness of the model using alpha = .05. Interpret the result in practical terms.
d) Test the temperature coefficient using alpha = .05.   Interpret the result in practical terms.
e) What information about this model does the coefficient of multiple determination provide?
f) Perform residual analysis to check the regression assumptions.
g) Predict, with 95% confidence, the collision claim amount for a month with an average temperature of 29°F and with 60% of claims by drivers under age 30.

Collision Claim ($), Pct Under 30 (%) & Temp (°F)

116250 50 31.5
217180 60.8 33
43436 45.1 45
159265 56.4 53.9
130308 53.3 63.9
72393 46.9 74.5
174740 57.8 79.4
101351 50.6 75.3
144787 55 68.7
28957 35.8 53.7
173744 57.9 47.6
86872 49.9 38.4
108420 51 28.7
203288 62.9 34.4
40658 45.1 43.9
149078 55.2 51.1
121973 53.7 63.4
67763 47.2 73
163130 56.1 80.5
94858 48.3 79.8
135525 54.7 68
27105 45.4 52.6
162631 56.5 48.9
81315 47.7 35.5

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