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.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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