Why doesn't "bx" come first in ŷ=a+bx, whereas "mx" comes first in y=mx+b.

I don't think the order matters as long as you have the correct value for the constant and slope.

Can anybody please explain why the constant coefficient 2.544 is the Y-intercept, and the caffeine coefficient 0.164 is the slope in the question 1? I can't seem to get my head around this. Please help!

The y-intercept is always displayed in the top row, and the slope is always displayed in the bottom row. (Unfortunately, I don't know the reasoning behind them - sorry! Generally, I've found that the slope, y-intercept, s, and r^2 are the most useful pieces of information in these data charts.)

I don't understand which is the x and y values on the charts

The constant is y which stands for number of hrs studied and the x is the number of milligrams of caffeine taken

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Interpreting computer output for regression

AP.STATS:

DAT‑1 (EU)

DAT‑1.G (LO)

Google Classroom

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

Question 1

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

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

(Choice A)
y, with, hat, on top, equals, 0, point, 164, plus, 2, point, 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, point, 544, plus, 0, point, 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

Question 2

Which statement about the slope is true?

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

(Choice A)
For each additional 1 hour of study time, the caffeine intake is predicted to increase by 0, point, 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, point, 164 hours.

question 3

Which statement about the y-intercept is true?

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

(Choice A)
When the caffeine intake is 0, start text, m, g, end text, the study time is predicted to be 2, point, 544 hours.
(Choice B)
When the study time is 0 hours, the caffeine intake is predicted to be 2, point, 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, point, 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, point, 544	0, point, 134	18, point, 955	0, point, 000
Caffeine (mg)	0, point, 164	0, point, 057	2, point, 862	0, point, 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, point, 544	0, point, 134	18, point, 955	0, point, 000
Caffeine (mg)	0, point, 164	0, point, 057	2, point, 862	0, point, 005

Question 6

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

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saikyun
Posted 6 years ago. Direct link to saikyun's post “In the earlier video, "R-...”
In the earlier video, "R-squared or coefficient of determination", you mentioned the SEline, as in, the sum of errors between the line and the points. Would the S (standard deviation in residuals" be SEline/n?
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(11 votes)
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Akira
Posted 2 years ago. Direct link to Akira's post “Why doesn't "bx" come fir...”
Why doesn't "bx" come first in ŷ=a+bx, whereas "mx" comes first in y=mx+b.
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(3 votes)
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- Sam Alarcon
  Posted 2 years ago. Direct link to Sam Alarcon's post “I don't think the order m...”
  I don't think the order matters as long as you have the correct value for the constant and slope.
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  (4 votes)
abojovic
Posted 3 years ago. Direct link to abojovic's post “I was under the impressio...”
I was under the impression if the Pvalue is below .05 that implies there is a relationship between the independent variable and the dependent variable. If there is also a positive relationship at what point can we confidently determine that the model is a good fit and the increase is caused by the independent variable. Is there a percent threshold for R-sqr/adj r-sqr?
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Won-jae Lee
Posted 3 years ago. Direct link to Won-jae Lee's post “Can anybody please explai...”
Can anybody please explain why the constant coefficient 2.544 is the Y-intercept, and the caffeine coefficient 0.164 is the slope in the question 1? I can't seem to get my head around this. Please help!
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(1 vote)
Answer
- taila
  Posted 3 years ago. Direct link to taila's post “The y-intercept is always...”
  The y-intercept is always displayed in the top row, and the slope is always displayed in the bottom row. (Unfortunately, I don't know the reasoning behind them - sorry! Generally, I've found that the slope, y-intercept, s, and r^2 are the most useful pieces of information in these data charts.)
  Button navigates to signup page
  (5 votes)
Adaugo Chikezie
Posted 4 years ago. Direct link to Adaugo Chikezie's post “I don't understand which ...”
I don't understand which is the x and y values on the charts
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(0 votes)
Answer
- Kelvin
  Posted 4 years ago. Direct link to Kelvin's post “The constant is y which s...”
  The constant is y which stands for number of hrs studied and the x is the number of milligrams of caffeine taken
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  (3 votes)
-PaperAngel-
Posted 9 months ago. Direct link to -PaperAngel-'s post “What does regression mean...”
What does regression mean?
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(1 vote)
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- Violet SW
  Posted 5 months ago. Direct link to Violet SW's post “Correlation quantifies th...”
  Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation.
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  (1 vote)
575368
Posted 5 months ago. Direct link to 575368's post “why is the format differe...”
why is the format different? We don't use y=mx+b but y=b+mx. Whats the difference?
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(1 vote)
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- var
  Posted 5 months ago. Direct link to var's post “there is no difference, s...”
  there is no difference, sometimes it's just written differently
  if you think of the commutative addition property, you can reorder the terms and the result won't change
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Maecie Rogahn
Posted 5 months ago. Direct link to Maecie Rogahn's post “more caffeine = more awak...”
more caffeine = more awake more willingness to study
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(1 vote)
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Owen Macquarrie
Posted 4 months ago. Direct link to Owen Macquarrie's post “Hello everyone!”
Hello everyone!
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Michael Wieland
Posted 6 months ago. Direct link to Michael Wieland's post “Don't know much about his...”
Don't know much about history
Don't know much biology
Don't know much about a science book
Don't know much about the French I took

But I do know that I love you
And I know that if you love me, too
What a wonderful world this would be

Don't know much about geography
Don't know much trigonometry
Don't know much about algebra
Don't know what a slide rule is for

But I do know one and one is two
And if this one could be with you
What a wonderful world this would be

Now, I don't claim to be an A student
But I'm trying to be
For maybe by being an A student, baby
I can win your love for me

Don't know much about history
Don't know much biology
Don't know much about a science book
Don't know much about the French I took

But I do know that I love you
And I know that if you love me, too
What a wonderful world this would be

La ta ta ta ta ta ta (History)
Hmm-mm-mm (Biology)
La ta ta ta ta ta ta (Science book)
Hmm-mm-mm (French I took)

Yeah, but I do know that I love you
And I know that if you love me, too
What a wonderful world this would be
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(0 votes)
Answer

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 5

Interpreting computer output for regression

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