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### 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:
PredictorCoefSE CoefTP
Constant$2,544$$0,134$$18,955$$0,000$
Caffeine (mg)$0,164$$0,057$$2,862$$0,005$
$S=1.532\phantom{\rule{1em}{0ex}}\text{R-Sq}=60.032\mathrm{%}\phantom{\rule{1em}{0ex}}\text{R-Sq(adj)}=58.621\mathrm{%}$
Pytanie 1
What is the equation of the least-squares regression line?
PredictorCoefSE CoefTP
Constant$2,544$$0,134$$18,955$$0,000$
Caffeine (mg)$0,164$$0,057$$2,862$$0,005$
$S=1.532\phantom{\rule{1em}{0ex}}\text{R-Sq}=60.032\mathrm{%}\phantom{\rule{1em}{0ex}}\text{R-Sq(adj)}=58.621\mathrm{%}$
Wybierz 1 odpowiedź:

Pytanie 2
Which statement about the slope is true?
PredictorCoefSE CoefTP
Constant$2,544$$0,134$$18,955$$0,000$
Caffeine (mg)$0,164$$0,057$$2,862$$0,005$
$S=1.532\phantom{\rule{1em}{0ex}}\text{R-Sq}=60.032\mathrm{%}\phantom{\rule{1em}{0ex}}\text{R-Sq(adj)}=58.621\mathrm{%}$
Wybierz 1 odpowiedź:

question 3
Which statement about the $y$-intercept is true?
PredictorCoefSE CoefTP
Constant$2,544$$0,134$$18,955$$0,000$
Caffeine (mg)$0,164$$0,057$$2,862$$0,005$
$S=1.532\phantom{\rule{1em}{0ex}}\text{R-Sq}=60.032\mathrm{%}\phantom{\rule{1em}{0ex}}\text{R-Sq(adj)}=58.621\mathrm{%}$
Wybierz 1 odpowiedź:

question 4
How large is a typical prediction error when using this model to predict study time from caffeine intake?
PredictorCoefSE CoefTP
Constant$2,544$$0,134$$18,955$$0,000$
Caffeine (mg)$0,164$$0,057$$2,862$$0,005$
$S=1.532\phantom{\rule{1em}{0ex}}\text{R-Sq}=60.032\mathrm{%}\phantom{\rule{1em}{0ex}}\text{R-Sq(adj)}=58.621\mathrm{%}$
Wybierz 1 odpowiedź:

question 5
About what percentage of the variation in study time can be explained by the regression on caffeine intake?
PredictorCoefSE CoefTP
Constant$2,544$$0,134$$18,955$$0,000$
Caffeine (mg)$0,164$$0,057$$2,862$$0,005$
$S=1.532\phantom{\rule{1em}{0ex}}\text{R-Sq}=60.032\mathrm{%}\phantom{\rule{1em}{0ex}}\text{R-Sq(adj)}=58.621\mathrm{%}$
Wybierz 1 odpowiedź:

Pytanie 6
Based on these data, can we conclude that consuming more caffeine will cause someone to study more?
Wybierz 1 odpowiedź:

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