Description based on excel data. Regression Analysis Output: 1. Solve the follow

Question

Description based on excel data.

Regression Analysis Output:

1. Solve the following questions: What is the relationship between saturated fat (sfat_dr) and alcohol consumption (alco_dr) for all groups? In addition, please state the hypotheses and explain in your own words what the answer means.

2. Please construct a simple regression with the dependent variable of alcohol consumption (alco_dr) and the independent variable as saturated fat (sfat_dr). What are the null and alternative hypotheses? Explain in your own words what the answer means. (*Graph is below.)

Simple Regression Graph:

3. Using the dataset, is there a total alcohol consumption (alco_dr) difference among the three groups? Please state the hypotheses and explain in your own words what the answer means.

Variable Column Description Format or Code Id sfat dr sfat ffo tfat dr tfat ffg alco dr alco ffg cal dr cal ffq 8-15 17-24 26-33 35-42 44-51 53-60 62-70 72-80 ID number Saturated fat-DR Saturated fat-FFQ Total fat-DR Total fat-FFQ Alcohol consumption-DR Alcohol consumption-FFQ Total calories-DR Total calories-FF

Explanation / Answer

Given that, the dependent variable of alcohol consumption (alco_dr) and the independent variable as saturated fat (sfat_dr).

We have given the regression output.

We can answer all the questions by using this output.

Solve the following questions: What is the relationship between saturated fat (sfat_dr) and alcohol consumption (alco_dr) for all groups?

Here we have to find correlation.

In the output Multiple R indicates that correlation value.

MultipleR = relationship between saturated fat (sfat_dr) and alcohol consumption (alco_dr) for all groups = 0.1814

Here correlation is positive indicates that there is positive relationship  between saturated fat (sfat_dr) and alcohol consumption (alco_dr) for all groups.

From the normal probability plot it indicates that the data follows normal distribution.

Tests of Hypothesis :

Here we can test the overall significance and individual significance.

Using the dataset, is there a total alcohol consumption (alco_dr) difference among the three groups? Please state the hypotheses and explain in your own words what the answer means

Overall significance :

Here we have to test the hypothesis that,

H0 : Bj = 0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Assume alpha = level of significance = 5% = 0.05

Here test statistic follows F-distribtution.

F = 5.82

P-value = 0.0169

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

We get significant result about overall significance.

Individual significance :

Here we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Assume alpha = level of significance = 5% = 0.05

Here test statistic follows t-distribtution.

t = 2.412

P-value = 0.0169

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

We get significant result about individual significance.

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