Now suppose our 806 students were a random sample from a much larger populations

Question

Now suppose our 806 students were a random sample from a much larger populations (say all Stat 100 students over the last 5 years). The multiple regression equation predicting skipped classes from both # of drinks per week and # sexual partners: Skipped Classes-0.1044 (Drinks) + 0.1317 (# Sex Partners) + Intercept fit our sample but how well would it fit the whole population? Before we go any further let's test whether either slope is significant. Maybe just using the average # of skipped classes works just as well for the whole population? You may think: Of course our regression equation works better, we calculated the slopes to fit the data better. But here's the point-we calculated them to fit our particular sample, but there's a lot of random jitter in our sample, maybe there's too much random itter and the error bars on our slopes are too big to work for other random samples. Our model is of the form: Y = 0 + 1X1 + 2X2 + error (where the assumption is that the errors are independent and N(0, 2) HO; All slopes-0. Same as Y = Y HA: At least one of the slopes 0. In other words, either | 0, or 2 0, or both0 a. Can we use either a Z or ttest here? Incorrect Yes, we can use a Z of a t test for the one-tail test but we must use Chi-Sqaure or F for the 2 tail test. Incorrect Yes, we can use Z= r/SE, for both slopes together just like we did for each separately in the simple regression. Correct: No, because we have more than one slope and we need a way to assess both of the slopes at the same time. Computer's answer now shown above. In b. The multiple correlation coefficient is R=0.3845. Compute the Chi-Square statistic to test the null hypothesis listed above. 2 = 139.83 Tries 2/2 Previous Tries Computer's answer now shown above. You are correct. r receipt no. is 162-1997 c. How many df for the Chi Square? 2 Computer's answer now shown above. You are correct. Previ r receipt no. is 162-2234 d. Find the p value for the Chi Square test using this online calculator 0 Computer's answer now shown above. In Tries 3/3 Previous Tries e. Now compute the F-stat. F Subrnit Answer Tries 2/3 Previous Tries f. How many degrees of freedom in the numerator?

Explanation / Answer

e) F = (R^2 /k) /(1-R^2)/(n-k-1)

here k = 2

n = 806

R = 0.3845

F =

f)

df numerator = k = 2

df denominator = n-k-1 = 803

g) p-value = 0.00000

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