Question

how do you know when a linear model is appropriate?

Answer 1

Because a linear regression model is not always appropriate for the data, you should assess the appropriateness of the model by defining residuals and examining residual plots.

Residuals
The difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e). Each data point has one residual.

Residual = Observed value - Predicted value
e = y - ŷ

Both the sum and the mean of the residuals are equal to zero. That is, Σ e = 0 and e = 0.

Answer 2

the residual shows an even scattering, or should i say normal

Answer 3

and the correlation coefficient is 0.981

Answer 4

@campbell_st @dan815

Answer 5

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.

Answer 6

so if the residual plot looks normal (evenly distributed) then a linear regression model is appropriate? @Prosper2win

Answer 7

yeah

Answer 8

so the correlation coefficient has nothing tot do with it?

Answer 9

@Prosper2win

Answer 10

???/ @Prosper2win

Answer 11

now I'm confused sorry

Answer 12

does the correlation coefficient come into play when decide ding if its a linear model or no

Answer 13

@jim_thompson5910

Answer 14

Yes I think so. If r = 1 or close to 1, then the points fall on a straight line or are near a straight line. This line has a positive slope.

For r = -1, it's the same story but with a negative slope

if r is close to 0, then the points are NOT going to all fall on/near a line. They are either randomly scattered or follow some other pattern such as a parabola.

Answer 15

so if the correlation coefficient is 0.981 its close to one meaning the points fall on a straight line or somewhat close aka a linear model would be appropriate? (in addition to the fact that the residual shows its evenly and randomly distributed)

Answer 16

yeah so it sounds like the points are close to a straight line with a positive slope

ie we have positive correlation

Answer 17

okay so answering the question "Is a linear model appropriate for modeling these data" with my answer above would be okay? @jim_thompson5910

Answer 18

yeah I think so

Answer 19

okay, would you mind helping me with a few other problems? @jim_thompson5910

Answer 20

sure, 2 more

Answer 21

Animal-waste lagoons and spray fields near aquatic environments may significantly degrade water quality and endanger health. The National Atmosphere Deposition Program has monitored the atmosphere ammonia at swine farms since 1978.The data on the swine population size (in thousands) and atmospheric ammonia (in paper million) for one decade are given below:
a) Construct a scatterplot for these data. (Find out from your instructor on how to submit your scatterplot).
b) The value for the correlation coefficient for these data is 0.85. Interpret this value.
c) Based on the scatterplot in part (a) and the value of the correlation coefficient in part (b), does it appear that the amount of atmospheric ammonia is linearly related to the swine population size? Explain.
d) What percent of the variability in atmospheric ammonia can be explained by swine population size?

Answer 22

what do you have for this one?

Answer 23

i have the scatterplot made (for a), and for b, i started to interpret the correlation coefficient of 0.85 saying that it is a strong positive linear relationship

Answer 24

I got a scatter plot with a line nearly going through or very close to all the points, so I agree

Answer 25

so for c would i be able to say yes the atmospheric ammonia appears to be linearly related to the swine population because you see a scatterplot with a line nearly going through or very close ton all the points

Answer 26

yes and it makes sense: the swine are creating the waste, so the more pigs, the more waste (and more ammonia)

Answer 27

okay, how would we do d?

Answer 28

compute r^2 to answer that question

Answer 29

.7225 so 72.25%?

Answer 30

correct, 72.25% of the variability is explained by the population of pigs while the remaining 27.75% is explained by other unknown factors

Answer 31

okay, last one

Answer 32

When children and adolescents are discharged from the hospital the parents may still provide substantial care, such as the insertion of a feeding tube through the nose and down the esophagus into the stomach. It is difficult for parents to know how far to insert the tube, especially with rapidly growing infants. It may be possible for parents to measure their child's height and from that calculate the appropriate insertion length using a regression equation. At a major children's hospital, children and adolescents' heights and esophageal lengths were measured and a regression analysis performed. The data from this analysis is summarized below:
a) For a child with a height one standard deviation above the mean, what would be the predicted esophageal length?
b) What proportion of the variability in esophageal length is accounted for by the height of the children and adolescents?
c) From the information presented above, does it appear that the esophagus length can be accurately predicted from the height of young patients? Provide statistical evidence for your response.

Answer 33

"For a child with a height one standard deviation above the mean"

what is H in this case?

Answer 34

143.5

Answer 35

good

Answer 36

you plug that height into the regression equation given to find the predicted esophageal length

Answer 37

37.4495

Answer 38

got the same

Answer 39

ok b?

Answer 40

b) What proportion of the variability in esophageal length is accounted for by the height of the children and adolescents?

compute r^2

Answer 41

.990025

Answer 42

yep

Answer 43

okay c?

Answer 44

c) From the information presented above, does it appear that the esophagus length can be accurately predicted from the height of young patients? Provide statistical evidence for your response.

look at how close r is to 1

Answer 45

r is very close to one (only .005 away)

Answer 46

yes, so it's very strongly linearly correlated. Let's hope so since we're dealing with a medical procedure that could be dangerous/deadly. Having the right info is crucial.

Answer 47

wait what

Answer 48

you don't want to be making random guesses, you want to be accurate in medical stuff like this

Answer 49

okay

Answer 50

nvm I mentioned that

Answer 51

wait so what would i put for c

Answer 52

what you had is good

Answer 53

that its really close?

Answer 54

but it doesn't answer the question "does it appear that the esophagus length can be accurately predicted from the height of young patients?"

Answer 55

yeah it's close to 1, so the data points pretty much fall on the line or really close to it

so you can use that regression equation to determine the esophagus length based on the height pretty accurately

Answer 56

oh okay

Answer 57

thank you so much!!!

Answer 58

np