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You are interested in predicting a son's height in inches based on his father's height in inches. The slope of the regression line is 0.5 and the y-intercept is 35. In terms of the variables in this example, what does the slope represent

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Answer:

When the father's height increases by 1 inch, the son's height increases by 0,5 inches.

Step-by-step explanation:

We are given the following in the question:

Father's height in inches is independent variable and son's height in inches in the dependent variable.

Slope, m = 0.5

y-intercept = 35

We can write the regression equation as:

[tex]y(x)=mx + c[/tex]

[tex]y(x) = 0.5x + 35[/tex]

where x is father's height in inches and y(x) is the son's height in inches.

Interpretation of slope:

  • Slope represents the rate of change.
  • It states the change in y when the x changes by one unit

[tex]y(x+1)-y(x) = 0.5(x+1)+35-0.5x-35\\y(x+1)-y(x) = 0.5[/tex]

Thus, we can say when the father's height increases by 1 inch, the son's height increases by 0,5 inches.

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