Diems 25-30 Section 4.1 tn NW 17. An Unhealthy Commute (Refer to Problem 2 . The

Question

Diems 25-30 Section 4.1 tn NW 17. An Unhealthy Commute (Refer to Problem 2 . The following data represent commute times (in mi em 25, Section score on a well-being survey es) Commute Time (minutes), x Gallup-Healthways Well-Bein Index Composite Score, y 15 25 35 50 72 105 69.2 68.3 67.5 67.1 66.4 66.1 63.9 Source: The Gallup Organization (a) Find the least-squares regression line treating the commute time, r, as the explanatory variable and the index score, y,as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Predict the well-being index of a person whose commute is 30 minutes (d) Suppose Barbara has a 20-minute commute and scores 67.3 on the survey. Is Barbara more "well-off" than the typical individual who has a 20-minute commute?

Explanation / Answer

Question 17

Here least square regression line

so lets say line equation is y^ = a +bx

Here n = 7

and a and b = line constants.

so by formulas

a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

all the values are given above and putting all these values from the table, we get

a = [468.5 * 20809 - 307 * 20195.2] /[7 * 20809 - 3072] = 69.03

Here

b =  [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [7 * 20195.2 - 307 * 468.5] / [ 7 * 20809 - 3072] = -0.047

y^ = -0.047x + 69.03

(b) Here the slope = -0.047, that mean if we increase commute time of any random person by 1 minute, it will decrease the well being index (Health index) by 0.047 value.

Here intercept = 69.03, that means that if commute time of any random human being is zero minute or nil, that means his/her well being index is 69.03.

(c) If x = 30 minutes

y^ = -0.047x + 69.03

y^(30) = -0.047 * 30 + 69.03 = 67.62

(d) Predicted Well being index at x = 20 minutes

y^(20) = -0.047 * 20 + 69.03 = 68.09

Her actual score is 67.3 so he is not better than an individual who has 20 minute commute.

Commute time (x) Gallup - Healthways Well-Being Index Composite Score, y x^2 xy 5 69.2 25 346 15 68.3 225 1024.5 25 67.5 625 1687.5 35 67.1 1225 2348.5 50 66.4 2500 3320 72 66.1 5184 4759.2 105 63.9 11025 6709.5 Sum 307 468.5 20809 20195.2

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