Consider the following table containing the betting spreads and actual spreads from 15 randomly selected football g
games.
8/7
Betting 1 25 2
Actual
Betting vs Actual Spreads
321266 1
4
17 17 6 21 -5 5 10 7 3 14 6
9
Copy Data
Construct a 95% prediction interval for a betting spread of 4. Round your answers to two decimal places.
To construct a 95% prediction interval for a betting spread of 4, we can use the formula:
Prediction Interval = Betting Spread ± t * (Standard Error)
First, we need to calculate the Standard Error. The formula for the Standard Error is:
Standard Error = (Mean Squared Error / n)^(1/2)
Given the actual spreads: 321266, 1, 4, 17, 17, 6, 21, -5, 5, 10, 7, 3, 14, 6, and 9, we can calculate the Mean Squared Error as follows:
Mean Squared Error = (321266^2 + 1^2 + 4^2 + 17^2 + 17^2 + 6^2 + 21^2 + (-5)^2 + 5^2 + 10^2 + 7^2 + 3^2 + 14^2 + 6^2 + 9^2) / 15
Mean Squared Error = 166440.9333
Next, we calculate the Standard Error:
Standard Error = (166440.9333 / 15)^(1/2)
Standard Error = 134.255
Next, we need to look up the t-value for a 95% confidence level and 14 degrees of freedom. Using a t-table, we find that the t-value is approximately 2.145.
Finally, we can calculate the Prediction Interval:
Prediction Interval = 4 ± 2.145 * 134.255
Prediction Interval = -280.83 to 288.83
Rounded to two decimal places, the 95% prediction interval for a betting spread of 4 is -280.83 to 288.83.