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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	$2,544$ ‍	$0,134$ ‍	$18,955$ ‍	$0,000$ ‍
Caffeine (mg)	$0,164$ ‍	$0,057$ ‍	$2,862$ ‍	$0,005$ ‍

S = 1.532 R-Sq = 60.032 % R-Sq(adj) = 58.621 %

Pytanie 1

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

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

S = 1.532 R-Sq = 60.032 % R-Sq(adj) = 58.621 %

(Choice A)
$\hat{y} = 0,164 + 2,544 x$ ‍, where $x$ ‍ represents caffeine intake and $y$ ‍ represents hours spent studying
(Choice B)
$\hat{y} = 0.164 + 2.544 x$ ‍, where $x$ ‍ represents hours spent studying and $y$ ‍ represents caffeine intake
(Choice C)
$\hat{y} = 2,544 + 0,164 x$ ‍, where $x$ ‍ represents caffeine intake and $y$ ‍ represents hours spent studying
(Choice D)
$\hat{y} = 2.544 + 0.164 x$ ‍, 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	$2,544$ ‍	$0,134$ ‍	$18,955$ ‍	$0,000$ ‍
Caffeine (mg)	$0,164$ ‍	$0,057$ ‍	$2,862$ ‍	$0,005$ ‍

S = 1.532 R-Sq = 60.032 % R-Sq(adj) = 58.621 %

(Choice A)
For each additional $1$ ‍ hour of study time, the caffeine intake is predicted to increase by $0,164 mg$ ‍.
(Choice B)
For each additional $1$ ‍ hour of study time, the caffeine intake is predicted to decrease by $0.164 mg$ ‍..
(Choice C)
For each additional $1 mg$ ‍ of caffeine, the study time is predicted to increase by $0.164$ ‍ hours.
(Choice D)
For each additional $1 mg$ ‍ of caffeine, the study time is predicted to decrease by $0,164$ ‍ hours.

question 3

Which statement about the $y$ ‍-intercept is true?

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

S = 1.532 R-Sq = 60.032 % R-Sq(adj) = 58.621 %

(Choice A)
When the caffeine intake is $0 mg$ ‍, the study time is predicted to be $2,544$ ‍ hours.
(Choice B)
When the study time is $0$ ‍ hours, the caffeine intake is predicted to be $2,544 mg$ ‍.
(Choice C)
When the caffeine intake is $0 mg$ ‍, the study time is predicted to be $0,164$ ‍ hours.
(Choice D)
When the study time is $0$ ‍ hours, the caffeine intake is predicted to be $0.164 mg$ ‍.

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	$2,544$ ‍	$0,134$ ‍	$18,955$ ‍	$0,000$ ‍
Caffeine (mg)	$0,164$ ‍	$0,057$ ‍	$2,862$ ‍	$0,005$ ‍

S = 1.532 R-Sq = 60.032 % R-Sq(adj) = 58.621 %

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	$2,544$ ‍	$0,134$ ‍	$18,955$ ‍	$0,000$ ‍
Caffeine (mg)	$0,164$ ‍	$0,057$ ‍	$2,862$ ‍	$0,005$ ‍

S = 1.532 R-Sq = 60.032 % R-Sq(adj) = 58.621 %

Pytanie 6

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

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