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trasher [3.6K]
3 years ago
13

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: ŷ = 13

5 + 6x. This implies that if the height is increased by 1 inch, the weight is expected to increase by
an average of 6 pounds.
Mathematics
1 answer:
Lunna [17]3 years ago
3 0

Answer:

y=6x +135

And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.

For the intercept of 135 represent the amount initial amount of weight for the scale.

Step-by-step explanation:

We assume that they use least squares in order to create the regression equation

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

With these we can find the sums:

And the slope would be:

m=6

The means for x and y are given by:

\bar x= \frac{\sum x_i}{n}

\bar y= \frac{\sum y_i}{n}

And we can find the intercept using this:

b=\bar y -m \bar x

For this case we know that the line adjusted is:

y=6x +135

And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.

For the intercept of 135 represent the amount initial amount of weight for the scale.

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