A number of different factors can contribute to the temperature of a city during

Question

A number of different factors can contribute to the temperature of a city during the summer months. We take a random sample of 24 cities across the United States and record their latitude, longitude, average annual precipitation (in inches), and altitude (in feet) for use as predictors of the average high temperature during the month of July. Use the output to analyze the relationship between average July high temperature and the four predictor variables. Write the linear model. Be sure to define each of the variables. Write the equation of the regression line. Interpret the slope coefficient for latitude. What is the predicted average high temperature in July for a city at 37 degrees north latitude and 97 degrees west longitude that sits 1300 feet above sea level and gets an average of 33 inches of precipitation each year? Write the hypotheses for testing if all of the slope parameters in the model are simultaneously equal to zero or not Use a 5% level of significance for this test. What are the values of the test statistic and p-value for the hypotheses in part (e)? Write a conclusion in the context of the problem using your observations from parts (e) and (f). Fill in the table with all of the appropriate information to determine which individual predictors are significant and which are not at the 5% level of significance. Which variables should you leave in the model and which should you remove?

Explanation / Answer

a) The linear model is Y=b0+b1x+...+bkxk+e, where, Y is the response variable, b0 is Y intercept, and b1...bk are coefficients of predictor variables.

b) Average high temperature=137.34-0.859 Latitude-0.204Longitude+0.004 Attitude-0.079 Annual precipitation

c) On any given annual precipitation, altitude, longitude, for 1 unit decrase in latitude, the average high temperature for July is 0.859.

d) Substitue, the value sin equation b) and obtain the average high temeparture.

Average high temperature=137.34-0.859*37-0.204*97+0.004*1300-0.079*33

=88.362

e) H0:beta1=beta2=beta3=beta4=0 (the model itself contributes nothing useful and all slope coefficients are zero)

H1: At least one of the betaj is not zero.

The F ratio is 4.936 and p value is too small, therefore, reject null hypothesis at alpha=0.05, to cocnlude that jth variable make sa useful contribution to the model, Betaj not equal to 0.

f) F test statistic and p value is 0.007

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