Question

In: Math

A)Test for significance of the Coefficient of Determination (F-test using α = 5%) B) Construct and...

A)Test for significance of the Coefficient of Determination (F-test using α = 5%)

B) Construct and interpret the confidence interval for the population regression coefficient b1 (use 1-α = 95%). Data set below and Thanks!

Unemployment Inflation
4.0 3.0
4.1 4.1
4.0 5.9
3.8 -0.6
4.0 1.8
4.0 5.8
4.0 2.9
4.1 0.0
3.9 5.2
3.9 1.7
3.9 1.7
3.9 2.3
4.2 5.7
4.2 2.3
4.3 0.6
4.4 1.7
4.3 5.1
4.5 2.3
4.6 -1.7
4.9 0.0
5.0 4.0
5.3 -2.8
5.5 -0.6
5.7 -0.6
5.7 1.7
5.7 1.7
5.7 3.4
5.9 3.9
5.8 0.6
5.8 1.1
5.8 2.2
5.7 2.8
5.7 1.7
5.7 2.2
5.9 1.7
6.0 1.1
5.8 3.3
5.9 5.5
5.9 4.4
6.0 -4.4
6.1 -0.6
6.3 1.1
6.2 2.2
6.1 3.8
6.1 2.7
6.0 -0.5
5.9 -1.1
5.7 2.2
5.7 4.3
5.6 3.2
5.7 4.3
5.5 1.1
5.6 5.9
5.6 3.2
5.5 0.0
5.4 1.1
5.4 1.6
5.4 5.8
5.4 2.1
5.4 0.0
5.2 1.1
5.4 3.7
5.1 5.7
5.1 4.7
5.1 -0.5
5.0 -0.5
5.0 6.2
4.9 5.6
5.1 12.2
4.9 2.5
5.0 -6.5
4.9 -0.5

Solutions

Expert Solution

Independent variable, X: Unemployment

Dependent variable, Y: Inflation

Following is the output of regression analysis;

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.127383261
R Square 0.016226495
Adjusted R Square 0.002172588
Standard Error 2.7536036
Observations 72
ANOVA
df SS MS F Significance F
Regression 1 8.75448263 8.75448263 1.154589606 0.286280391
Residual 70 530.7632951 7.582332788
Total 71 539.5177778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 4.693261456 2.337815171 2.007541706 0.048553722 0.030636179 9.355886732
Unemployment, X -0.480458221 0.447138234 -1.074518314 0.286280391 -1.372247297 0.411330855

A)

The R-square is:

R -square = 0.0162

Here hypotheses are:

F-test statistics for coefficient of determination is

The p-value is: 0.2863

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

B)

Here we have

Degree of freedom: df=n-2=70

The critical value of t for 95% confidence interval using excel function "=TINV(0.05,70)" is: 1.994.

The 95% confidence interval for slope is:


Related Solutions

A)Test the significance of the population correlation coefficient r (t-test using        α = 5%) B)Test the...
A)Test the significance of the population correlation coefficient r (t-test using        α = 5%) B)Test the significance of the population regression coefficient b1 (t-test using        α = 5%) C)Interpret the Coefficient of Determination as measure of the goodness of the fit (R2). Data sets are below and Thanks! Unemployment Inflation 4.0 3.0 4.1 4.1 4.0 5.9 3.8 -0.6 4.0 1.8 4.0 5.8 4.0 2.9 4.1 0.0 3.9 5.2 3.9 1.7 3.9 1.7 3.9 2.3 4.2 5.7 4.2 2.3 4.3 0.6...
Assume that you plan to use a significance level of α = 0.05 to test 5)...
Assume that you plan to use a significance level of α = 0.05 to test 5) the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test, and make a conclusion addressed to the claim. n1=100 n2=100 x1 = 38 x2 = 40
Assume that a hypothesis test will be conducted using significance level α = .01 and alternative...
Assume that a hypothesis test will be conducted using significance level α = .01 and alternative hypothesis Ha: μ : ≠ 19.3. Furthermore, we will use the following sample data: n = 12, x-bar = 18.8, and s = 2.1.
In simple linear regression, r 2 is the _____. a. coefficient of determination b. coefficient of...
In simple linear regression, r 2 is the _____. a. coefficient of determination b. coefficient of correlation c. estimated regression equation d. sum of the squared residuals QUESTION 3 A least squares regression line ______. a. may be used to predict a value of y if the corresponding x value is given b. implies a cause-effect relationship between x and y c. can only be determined if a good linear relationship exists between x and y d. All of the...
When we carry out a statistical test with significance level α = 5%, the probability of...
When we carry out a statistical test with significance level α = 5%, the probability of rejecting the null hypothesis when it is true is 5%. Suppose that we independently select 5 random samples of size 100, and for each sample carry out the same statistical test with significance level 5%. We know that the null hypothesis is true. What is the probability that we reject the null hypothesis at most once out of the 5 tests?
Test the given claim using the α=0.05 significance level and assuming that the populations are normally...
Test the given claim using the α=0.05 significance level and assuming that the populations are normally distributed and that the population variances are equal. Claim: The treatment population and the placebo population have the same means. Treatment group: n=9, x¯=110, s=5.9. Placebo group: n=7, x¯=116,s=5.7. The test statistic is =___________ The positive critical value is =__________ The negative critical value is =________ Is there sufficient evidence to warrant the rejection of the claim that the treatment and placebo populations have...
Conduct a test and find if there is a difference at the α=0.01 level of significance....
Conduct a test and find if there is a difference at the α=0.01 level of significance. In​randomized, double-blind clinical trials of a new vaccine, children were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the first dose, 67 of 607 subjects in the experimental group (group 1) experienced fever as a side effect. After the first dose, 109 of 728 subjects in the control group​...
Test to see if the population correlation coefficient is not equal to zero using significance of 0.05. What are your conclusions?
Consider the following X:            4              7              2              6              6 Y:            6              9              5              5              7 Using XLS, calculate the correlation coefficient for this sample. Test to see if the population correlation coefficient is not equal to zero using significance of 0.05. What are your conclusions?
In order to test ?0:?=.5 vs. ??:?<.5 using the .10 level of significance, a sample of...
In order to test ?0:?=.5 vs. ??:?<.5 using the .10 level of significance, a sample of ?=100 will be selected. Suppose that, in reality, the population proportion is .4. (a) The probability the test will commit a type II error is   .___ (b) The power of the test is ___ . Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 30 and 25 successes, respectively. Test ?0:(?1−?2)=0 against ??:(?1−?2)≠0. Use...
Show how; Independent t-test , Coefficient of determination, Exploratory factor analysis, Chi-square test, Correlation coefficient, R-squared...
Show how; Independent t-test , Coefficient of determination, Exploratory factor analysis, Chi-square test, Correlation coefficient, R-squared value, Analysis of covariance, Analysis of variance are applied in analysis of quantitative data ( explain in simple English please)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT