Multiple Regression Analysis Suppose you\'ve been asked by the Oregon Football t

Question

Multiple Regression Analysis Suppose you've been asked by the Oregon Football team to evaluate attendance. After some research on the topic, you decide on the following multiple linear regression model: Att_i = beta_1 + beta_2 Win_i + beta_3 Con f_i + beta_4 Nu m_i + beta_5 T emp_i + u_i where Att_i is the attendance at the ith game, Win_i is the winning percentage of the opponent in the ith game, Con f_i represents the winning percentage of the opposing team's conference, Num_i represents the sequential order of this game in the current season, and Temp_i is a variable which contains the temperature in degrees Fahrenheit for game i. You collect data on 130 games for all of the above variables and estimate the model via OLS. You obtain the following estimates and associated standard errors: (a) Interpret the parameter estimates beta_2 and beta_5. (b) Suppose you want to test the null hypothesis that the sequential order of the game has no effect on game attendance. Use a 5% and 1% level of significance. You need to report the null and alternative hypothesis, the test statistic, the degrees of freedom, the critical value, and the result of the test. Parameter Estimate Standard Error beta_1 12000 100000 beta_2 8500 2250 beta_3 2500 1500 beta_4 -3200 1550 beta_5 400 275 (c) Suppose you want to test the null hypothesis that the variable temp has a positive effect on game attendance. Motivate and conduct a one-sided hypothesis test of this null hypothesis. Use the 5% significance level. Your answer should include the null and alternative hypothesis, the test statistic, the degrees of freedom, the critical value, and the result of the test. (d) Because the Ducks have such loyal fans, you don't think that winning percentage or conference winning percentage has any effect on attendance. You decide to test that these coefficients are jointly equal to 0. If the RSS on the previous model was 48202 and the RSS on the new model is 58392, conduct the F-test at the 5% level. Your answer should include the null and alternative hypotheses, the test statistic, the degrees of freedom, the F critical value and the result of the test.

Explanation / Answer

Solution:

a) b2^ is change in the attendance if winning % of opponent increases by 1 unit

similarly b5^ is change in attendance if temperature increses by 1 Fahrenheit

b) b4 - coefficient of Num (sequential order}

TS = -3200/1550 = -2.064516

df= n-k-1 = 130 - 5-1 = 124

critical value= 1.979 for 5 % level of significance

and 2.616 for 1%

hence the variable is significant at 5 % ,but not at 1 %

c)

Ho : b5 = 0

Ha:b5 > 0

TS = 400/275 = 1.4545

critical value = 1.657

since tS <critical value

hence we reject the null

d) Ts = (SSR_r - SSR_ur)/q)/(SSR_ur)/(n-k-1))

= ((58392 - 48202)/2) /( 48202/ 124) = 13.10692

df1 = 2 ,df2 = 124

critical value = 3.07

since TS> critical value we reject the null and conclude that winningand conference winning has significant effect jointly

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