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Statystyka - program rozszerzony

Kurs: Statystyka - program rozszerzony > Rozdział 5

Lekcja 4: Ocenianie dopasowania w regresji z użyciem metody najmniejszych kwadratów

Interpretowanie komputerowego wyniku regresji

Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship.

This is computer output from a least-squares regression analysis on the data:

Predictor	Coef	SE Coef	T	P
Constant	2, comma, 544	0, comma, 134	18, comma, 955	0, comma, 000
Caffeine (mg)	0, comma, 164	0, comma, 057	2, comma, 862	0, comma, 005

S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent

Pytanie 1

What is the equation of the least-squares regression line?

Predictor	Coef	SE Coef	T	P
Constant	2, comma, 544	0, comma, 134	18, comma, 955	0, comma, 000
Caffeine (mg)	0, comma, 164	0, comma, 057	2, comma, 862	0, comma, 005

(Choice A)
y, with, hat, on top, equals, 0, comma, 164, plus, 2, comma, 544, x, where x represents caffeine intake and y represents hours spent studying
(Choice B)
y, with, hat, on top, equals, 0, point, 164, plus, 2, point, 544, x, where x represents hours spent studying and y represents caffeine intake
(Choice C)
y, with, hat, on top, equals, 2, comma, 544, plus, 0, comma, 164, x, where x represents caffeine intake and y represents hours spent studying
(Choice D)
y, with, hat, on top, equals, 2, point, 544, plus, 0, point, 164, x, where x represents hours spent studying and y represents caffeine intake

Pytanie 2

Which statement about the slope is true?

Predictor	Coef	SE Coef	T	P
Constant	2, comma, 544	0, comma, 134	18, comma, 955	0, comma, 000
Caffeine (mg)	0, comma, 164	0, comma, 057	2, comma, 862	0, comma, 005

(Choice A)
For each additional 1 hour of study time, the caffeine intake is predicted to increase by 0, comma, 164, start text, m, g, end text.
(Choice B)
For each additional 1 hour of study time, the caffeine intake is predicted to decrease by 0, point, 164, start text, m, g, end text..
(Choice C)
For each additional 1, start text, m, g, end text of caffeine, the study time is predicted to increase by 0, point, 164 hours.
(Choice D)
For each additional 1, start text, m, g, end text of caffeine, the study time is predicted to decrease by 0, comma, 164 hours.

question 3

Which statement about the y-intercept is true?

Predictor	Coef	SE Coef	T	P
Constant	2, comma, 544	0, comma, 134	18, comma, 955	0, comma, 000
Caffeine (mg)	0, comma, 164	0, comma, 057	2, comma, 862	0, comma, 005

(Choice A)
When the caffeine intake is 0, start text, m, g, end text, the study time is predicted to be 2, comma, 544 hours.
(Choice B)
When the study time is 0 hours, the caffeine intake is predicted to be 2, comma, 544, start text, m, g, end text.
(Choice C)
When the caffeine intake is 0, start text, m, g, end text, the study time is predicted to be 0, comma, 164 hours.
(Choice D)
When the study time is 0 hours, the caffeine intake is predicted to be 0, point, 164, start text, m, g, end text.

question 4

How large is a typical prediction error when using this model to predict study time from caffeine intake?

Predictor	Coef	SE Coef	T	P
Constant	2, comma, 544	0, comma, 134	18, comma, 955	0, comma, 000
Caffeine (mg)	0, comma, 164	0, comma, 057	2, comma, 862	0, comma, 005

question 5

About what percentage of the variation in study time can be explained by the regression on caffeine intake?

Predictor	Coef	SE Coef	T	P
Constant	2, comma, 544	0, comma, 134	18, comma, 955	0, comma, 000
Caffeine (mg)	0, comma, 164	0, comma, 057	2, comma, 862	0, comma, 005

Pytanie 6

Based on these data, can we conclude that consuming more caffeine will cause someone to study more?

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