7. Sometimes it’s scary to ask people out on dates, and sometimes it’s easier. A

Question

7. Sometimes it’s scary to ask people out on dates, and sometimes it’s easier. A dating researcher decides to try to build a model to predict how likely a person is to ask someone on a date based on the following predictors: level of attraction, amount of loneliness, desperation, fear of rejection. How many parameters are in the model?

8. After 20 observations, the model predicting how likely a person is to ask someone on a date based on level of attraction, amount of loneliness, desperation and fear of rejection has an error sum of squares of 10.6 and a total sum of squares of 26.2. What is the F-test statistic?

9. Your null hypothesis was that the regression coefficients for level of attraction, amount of loneliness, desperation and fear of rejection are all 0. What is the threshold value above which the F-statistic must lie in order to reject the null hypothesis at the 0.05 level? Use the F-table in the formulas and tables document and round the value to three decimal places.

Explanation / Answer

(7) There are 4 parameters in the model namely level of attraction, amount of loneliness, desperation, fear of rejection.

(8) n = 20, m = 4

SSError = 10.6, dfError = n-m = 20-4 = 16

SSTotal = 26.2

SSFactor = SSTotal - SSError = 26.2 - 20.6 = 5.6

dfFactor = m-1 = 4-1 = 3

F-test statistic = (SSFactor/dfFactor)/(SSError/dfError)

= (5.6/3)/(10.6/16)

= 1.8666/0.6625

F-test statistic = 2.8175

(9) FCritical = 3.24

As F-test statistic < FCritical, we will reject the null.

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