1. Researchers are studying the effect of alcohol consumption on a person's short-term memory. Six volunteer subjects are assigned to consume a certain number of drinks X. A short time later, the subjects are given a memory test, and their score Y on the test is recorded. The data are shown below, together with the means and standard deviations:
Subject 1 2 3 4 5 6 mean std dev
No. of Drinks 4 2 8 3 1 6 4 2.61
Test Score 81 90 22 58 80 53 64 25.07
The correlation between number of drinks and test score is calculated to be r = 0.869.
(a) What fraction of the variation in test score can be accounted for by its regression on number of drinks consumed?
(b) Find the equation of the least squares regression line.
(c) Find the predicted test scores for a subject who consumes 5 drinks and for a subject who consumes 11 drinks.
(d) Is one of your predictions in (c) more reliable than the other? Explain.
a)
R² = 0.7550
Approximately 75.50% variation in test
score can be accounted for by its regression on number of drinks
consumed
b)
| ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
| total sum | 24.00 | 384.00 | 34.00 | 3142.00 | -284.00 |
| mean | 4.00 | 64.00 | SSxx | SSyy | SSxy |
sample size , n = 6
here, x̅ = Σx / n= 4.000
ȳ = Σy/n = 64.000
SSxx = Σ(x-x̅)² = 34.0000
SSxy= Σ(x-x̅)(y-ȳ) = -284.0
estimated slope , ß1 = SSxy/SSxx = -284/34=
-8.35294
intercept,ß0 = y̅-ß1* x̄ = 64- (-8.3529
)*4= 97.41176
Regression line is, Ŷ= 97.412 +
( -8.353 )*x
......
c)
Predicted Y at X= 5
is
Ŷ= 97.4118 +
-8.3529 *5= 55.65
Predicted Y at X= 11 is
Ŷ= 97.4118 +
-8.3529 *11= 5.53
...........
d)
55.65 i more relable than other
as for 11 drinks it is extrapollated valeu
........
thanks
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1. Researchers are studying the effect of alcohol consumption on a person's short-term memory. Six volunteer...