This set of questions is based on body dimension data collected on 201 statistic

Question

This set of questions is based on body dimension data collected on 201 statistics students in 2001. The variables of interest for this question are stated below.

1) What percent of the variability in weight is explained by the model (i.e. the 3 predictor variables)?

2) Interpret the coefficient of calf.

3) At the 0.05 significance level, is calf a significant predictor for weight after accounting for shoe size and handspan? Do i and ii below:

i) State the null hypothesis using a parameter.

ii) State the test statistic and conclusion.

4) Is there concern for multicollinearity in this model? (Refer to 2 elements from the output in your answer.

1) weight weight in pounds 1) in 2) shoe shoe size 3) handspan span of hand in inches 4) calf calf circumference in inches. Information on the data and the model fi in R are shown below names (dim. data) [1] weight shoe handspan. calf cor dim. data) shoe handspan calf weight weight 1.0000000 0.5883658 0.5390747 0.6476550 shoe 0.5883658 1.0000000 0.5684123 0.4101189 hand span 0.5390747 0.5684123 1.0000000 0.3322298 0.6476550 0.4101189 0.3322298 1.0000000 calf

Explanation / Answer

1) What percent of the variability in weight is explained by the model (i.e. the 3 predictor variables)?

The coefficient of determination or the value of the R square is given as 0.5814 which means about 58.14% of the variation in the dependent variable or response variable weight is explained by the model or the independent variables or predictors shoe, handspan and calf.

2) Interpret the coefficient of calf.

The coefficient of calf is given as 8.5575, which is positive in nature and it indicate the increase in the weight as per unit increase in the value for calf.

3) At the 0.05 significance level, is calf a significant predictor for weight after accounting for shoe size and hand span? Do i and ii below:

i) State the null hypothesis using a parameter.

Here, we have to test for the coefficient of regression for the predictor Calf. We have test for the population parameter 3. The null and alternative hypotheses are given as below:

H0: 3 = 0 V/s Ha: 3 0

ii) State the test statistic and conclusion.

Here, we have to use the t test for checking whether the calf is a significant predictor for the prediction of weight or not. The test statistic is given as below:

t = b1/SE(b1) = 8.5575/0.9475 = 9.032

df = 197

P-value = 0.00

= 0.05

P-value <

So, we reject the null hypothesis that the given predictor is not statistically significant.

This means we conclude that there is sufficient evidence that the predictor calf is a statistically significant predictor for the prediction of weight.

4) Is there concern for multicollinearity in this model? (Refer to 2 elements from the output in your answer.

There is no concern for multicollinearity in this model because the all values for the vif are less than 5.

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