Answer:
a)
Where:
And the slope would be:
And we can find the intercept using this:
So then the linear model would be:
b) > x<-c(29.67, 29.87, 30.15, 30.21, 30.47, 30.64, 30.80)
> y<-c(2.64,2.59, 2.69, 2.60, 2.48, 2.38, 2.25)
> lm<- lm(y~x)
> lm
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
12.5009 -0.3299
And the model is given by:
c) Every increase of one degree Celsius means about -0.330 fewer mean millimeters of coral growth per year.
Step-by-step explanation:
For this case we have the following data:
X: 29.67 29.87 30.15 30.21 30.47 30.64 30.80
Y: 2.64 2.59 2.69 2.60 2.48 2.38 2.25
Part a
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
For our case we have this:
n=7
We can calculate the slope for the regression model with this formula:
Where:
And if we replace we got:
And the slope would be:
And we can find the intercept using this:
So then the linear model would be:
Part b
For this case we use the following R code:
> x<-c(29.67, 29.87, 30.15, 30.21, 30.47, 30.64, 30.80)
> y<-c(2.64,2.59, 2.69, 2.60, 2.48, 2.38, 2.25)
> lm<- lm(y~x)
> lm
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
12.5009 -0.3299
And the model is given by:
Part c
For this case the best interpretation is:
Every increase of one degree Celsius means about -0.330 fewer mean millimeters of coral growth per year.