Question

A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 14 12 27 14 12 11 11 30 22 Money 65 24 79 61 48 32 55 114 77

Time	14	12	27	14	12	11	11	30	22
Money	65	24	79	61	48	32	55	114	77

y=6.95+3.22x

Interpret the y-intercept in the context of the question:

• The average amount of money spent is predicted to be $6.95.
• If a customer spends no time at the store, then that customer will spend $6.95.
• The y-intercept has no practical meaning for this study. <<<<<<<Correct Answer>>>>>
• The best prediction for a customer who doesn't spend any time at the store is that the customer will spend $6.95.

I know the answer but do not understand the process, please explain

Answer 1

The equation of line of regression is

where

=6.95

=3.22

Thus

6.95 + 3.22 x

where

3.22 is the estimate of slope

6.95 is the estimate of y intercept .

It is the value of y when x=0 , that is money spent when the customer spends no time in the store , which has no practical significance ( as we cannot spend money without spending time in the store)  , but mathematically , it is the point (0, 6.95) where  regression line touches y axis , thus it is called y intercept . ( see the graph below)

Interpretation of y -intercept

The y intercept has no practical meaning for this study.  

calculation :

	x	y	x^2	y^2	xy
	14	65	196	4225	910
	12	24	144	576	288
	27	79	729	6241	2133
	14	61	196	3721	854
	12	48	144	2304	576
	11	32	121	1024	352
	11	55	121	3025	605
	30	114	900	12996	3420
	22	77	484	5929	1694
total	153	555	3035	40041	10832