The correlation coefficient,
r , tells us about the strength and direction of the linear relationship between
x and
y . However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at both the value of the correlation coefficient
r and the sample size
n , together.
We perform a hypothesis test of the
"significance of the correlation coefficient" to decide whether the linear relationship in the sample data is strong enough to use to model the relationship in the population.
The sample data are used to compute
r , the correlation coefficient for the sample. If we had data for the entire population, we could find the population correlation coefficient. But because we have only have sample data, we cannot calculate the population correlation coefficient. The sample correlation coefficient,
r , is our estimate of the unknown population correlation coefficient.
The symbol for the population correlation coefficient is
ρ , the Greek letter "rho."
ρ = population correlation coefficient (unknown)
r = sample correlation coefficient (known; calculated from sample data)
The hypothesis test lets us decide whether the value of the population correlation coefficient
ρ is "close to zero" or "significantly different from zero". We decide this based on the sample correlation coefficient
r and the sample size
n .
If the test concludes that the correlation coefficient is significantly different from zero, we say that the correlation coefficient is "significant."
Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between
x and
y because the correlation coefficient is significantly different from zero.
What the conclusion means: There is a significant linear relationship between
x and
y . We can use the regression line to model the linear relationship between
x and
y in the population.
If the test concludes that the correlation coefficient is not significantly different from zero (it is close to zero), we say that correlation coefficient is "not significant".
Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between
x and
y because the correlation coefficient is not significantly different from zero."
What the conclusion means: There is not a significant linear relationship between
x and
y . Therefore, we CANNOT use the regression line to model a linear relationship between
x and
y in the population.
Note
If
r is significant and the scatter plot shows a linear trend, the line can be used to predict the value of
y for values of
x that are within the domain of observed
x values.
If
r is not significant OR if the scatter plot does not show a linear trend, the line should not be used for prediction.
If
r is significant and if the scatter plot shows a linear trend, the line may NOT be appropriate or reliable for prediction OUTSIDE the domain of observed
x values in the data.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.