Interpreting linear regression slope & y-intercept?

Question

This might be a dumb question .. but I do not understand how to interpret this linear regression equation problem:

Bottles of spring water are bundled in packages contatining 6, 12, or 25 bottles. The respect prices are given in the table below:

no. of bottles | price
--------------------------------
6 | $3.99
12 | $5.99
25 | $8.29

The linear regression (on ti-83 plus) comes out to be:

y = .2183745583x + 2.959964664

I know what the slope & y-intercept are from ax+b

but how do I interpret these numbers in terms of the situation (slope of the regression equation & y-intercept of the regression equation).

Thanks.

Answer 1

I am not sure about what you mean by your question but

y = Price
x = no. of bottles

With a linear regression, you fit a straight line through the data to determine the relationship of price vs. no. of bottles. The R^2 value is .97 meaning that the data does correlate to a linear fit (however with only 3 data points this does not mean much).

The slope (a) is approx. .218. This means that for each one bottle added, the price increases by $0.22. Also the intercept (b) ~ 2.96. This means that the price of zero bottles is $2.96. This most likely does not make sense for this case and the intercept should be forced to zero. However this makes the linear fit very poor and would lead to the conclusion that this data should not be correlated with a linear regression.

Answer 2

Y Intercept Of Regression Line

Answer 3

The estimated price is found by a base price of $2.96 plus $0.218 per bottle.

..6, $4.27 - $3.99 = 0.28
12, $5.58 - $5.99 =-0.41
25, $8.42 - $8.29 = 0.13

This is actually pretty typical of pricing approximations, indicating a "carton" price of $2.96 and a bottle price of 21.8 cents.

Answer 4

The Correlation Coefficient is your "r" value. The equation Y = .17x - 3.17 is the equivalent to Y = Mx + B This is the standard equation of a line Where M = Slope and B = Y Intercept