Null Hypothesis
H
0 : The population correlation coefficient IS NOT significantly different from zero. There IS NOT a significant linear relationship(correlation) between
x and
y in the population.
Alternate Hypothesis
H
a : The population correlation coefficient IS significantly DIFFERENT FROM zero. There IS A SIGNIFICANT LINEAR RELATIONSHIP (correlation) between
x and
y in the population.
Drawing a conclusion:
There are two methods of making the decision. The two methods are equivalent and give the same result.
Method 1: Using the
p -value
Method 2: Using a table of critical values
In this chapter of this textbook, we will always use a significance level of 5%,
α = 0.05
Note
Using the
p -value method, you could choose any appropriate significance level you want; you are not limited to using
α = 0.05. But the table of critical values provided in this textbook assumes that we are using a significance level of 5%,
α = 0.05. (If we wanted to use a different significance level than 5% with the critical value method, we would need different tables of critical values that are not provided in this textbook.)
Method 1: using a
p -value to make a decision
To calculate the
p -value using LinRegTTEST:
On the LinRegTTEST input screen, on the line prompt for
β or
ρ , highlight "
≠ 0 "
The output screen shows the p-value on the line that reads "p =".
(Most computer statistical software can calculate the
p -value.)
If the
p -value is less than the significance level (
α = 0.05):
Decision: Reject the null hypothesis.
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."
If the
p -value is not less than the significance level (
α = 0.05)
Decision: DO NOT REJECT the null hypothesis.
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."
Calculation notes:
You will use technology to calculate the
p -value. The following describes the calculations to compute the test statistics and the
p -value:
The
p -value is calculated using a
t -distribution with
n - 2 degrees of freedom.
The formula for the test statistic is
. The value of the test statistic,
t , is shown in the computer or calculator output along with the
p -value. The test statistic
t has the same sign as the correlation coefficient
r .
The
p -value is the combined area in both tails.
An alternative way to calculate the
p -value
(p) given by LinRegTTest is the command 2*tcdf(abs(t),10^99, n-2) in 2nd DISTR.
The line of best fit is: ŷ = -173.51 + 4.83
x with
r = 0.6631 and there are
n = 11 data points.
Can the regression line be used for prediction?
Given a third exam score (
x value), can we
use the line to predict the final exam score (predicted
y value)?
H
0 :
ρ = 0
H
a :
ρ ≠ 0
α = 0.05
The
p -value is 0.026 (from LinRegTTest on your calculator or from computer software).
The
p -value, 0.026, is less than the significance level of
α = 0.05.
Decision: Reject the Null Hypothesis
H
0
Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between the third exam score (
x ) and the final exam score (
y ) because the correlation coefficient is significantly different from zero.
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.