Using observations for 100 families on annual income(inc) and consumption(cons)

Question

Using observations   for 100 families on annual income(inc) and consumption(cons) (both measured in dollars),the   following   regression results are obtained:
cons = 124.84 + 0.853 inc, R^2= 0.692

a) Interpre the intercept in this equation, and comment on its sign and magnitude.
b) What is the predicted consumption when family income is $30,000?
c) If a family increases its income by $10,000, what is the regression model’s prediction for how this will affect the family’s consumption spending?

Please show work and equation! Thanks!

Explanation / Answer

(a)

Intercept : -124.84

It is negative and magnitude : 124.84

(b)

inc = $30,000

so the predicted consumption when family income is $30,000 is

cons = 124.84 + 0.853 30000= $25, 465.16

(c)

Since slope of the model is 0.853 so if a family increases its income by $10,000 then the family’s consumption spending is increased by $8,530.

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