Problem: Height is frequently named as a good predictor variable for weight among people of the same age and gender. The following are th e raw data and results of a regression analysis of the heights and weights of a sample of 14 males between the ages of 19 and 26 who participated in a study.

Answer the following

1. Write out the regression equation.
   Solution: Using SPSS and the data provided we obtain the following output:
   
   
   
   
   From the last table, we get the following regression equation:
   \[\hat{W}=-60.622+0.755\,H\]
   where \(\hat{W}\) represents the estimated weight and \(H\) represents the height.
2. 
   If you knew that the height of someone was 162.5, calculate the weight of that person.
   Solution: We use the regression equation to the predicted weight. We simply plug \(H=162.5\) into the last equation, which gives the following estimated weight
   \[\hat{W}=-60.622+0.755\times 162.5=62.0655\]
3. What information do you look at in the output to determine whether there is a statistically significant relationship between height and weight in this sample?

Solution: We look at the following table:

We are interested in \(R\) and \({{R}^{2}}\). The value \(R=0.689\) indicates a significant linear relationship between height and weight (for this \(R\) we reject the hypothesis that the actual correlation is zero). But in spite of the fact there a linear relationship, it’s not too strong. The value of \({{R}^{2}}=0.475\) implies that only 47.5% of the variation of the weight is explained by the linear regression.

HEIGHT (cm) WEIGHT ( kgs )
185      83.9
180      99.0
173      63.8
168      71.3
175      65.3
183      79.6
184      70.3
174      69.2
164      56.4
169      66.2
205      88.7
161      59.7
177      64.6
174      78.8

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Solution: The downloadable solution consists of 3 pages, 265 words and 5 charts.
Deliverable: Word Document