please help! Question: Suppose that a researcher wants to study whether eating m

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please help!

Question: Suppose that a researcher wants to study whether eating more chocolate can improve your health. T...

Suppose that a researcher wants to study whether eating more chocolate can improve your health. The researcher gathers data on characteristics of 1018 men and women aged 20 to 85 and runs the following regression:

BMIi = 0 + 1 Chocolate + 2 Female + 3 Age + 4 Activity + UI

Where BMI is body mass index,

Chocolate is the number of times a week that the person ate chocolate,

Female is a dummy for sex,

Age is age in years,

Activity is the number of times per week that the person engages in the vigorous activity.

The researcher estimated the coefficient on Chocolate to be-0.130 with a standard error of 0.053.

The stated conclusion is that "chocolate consumption reduces your BMI."

1. Assess the analysis and the conclusion.

2. Suggest any improvements you can come up with

Explanation / Answer

1).

Consider the given model,

BMIi = 0 + 1 Chocolate + 2 Female + 3 Age + 4 Activity + ui

Where BMI = body mass index, Chocolate = the number of times a week that the person ate chocolate,

Female = a dummy for sex, Age = age in years,

Activity = the number of times per week that the person engages in the vigorous activity.

We have also given that “1= (-0.13)”, => there is a negative relationship between “BMI” and “Chocolate”, and if “chocolate consumption increases by 1 time in a week, which implied the “BMI” index will fall by “0.13”.

2).

So, it is clear that there is negative relationship between “BMI” and “Chocolate”. Now one improvement that we come up is we can check whether the “Chocolate” variable is really a significant one and whether the model is a good one or not.     

So, we have given that “1= (-0.13)” and “SE(1)= 0.053”. So test statistic is given by,  

=> “t= 1/SE(1), = (-0.13) / 0.053 = (-2.4528)”. So, |t|=2.4528 > t(0.025, n-k) here a=5%. So, we can conclude that the “Chocolate” variable is significantly differ from zero at 5% level of significance.

Now, if the “R^2 > = 0.7”, we can conclude that the model is really a good model and the “chocolate” variable is significantly as well as negatively related to “BMI”.

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