Question

Problem 6-23 (Algorithmic) The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study. Year Percentage of Adults Who Exercise 30 or more minutes at least three times per week 1 41.8 2 45.4 3 47.2 4 45.7 5 46.8 6 44.8 7 47.8 8 50.5 9 48.3 10 49.3 11 49.5 12 52.5 13 50.7 14 55 15 52.3

Answer 1

--> The Health Benefits lth Benefits of Regular exercise but are. Adults Listening; Model graphi- Y-Referent 45+ 1 lo 3 6 9 12 15 X-independent * Regression Line - (ŷ =0.69X+42.98) * From the above plot, it shows increasing trend in the percentage of reporting adults as the year advances,

Excel output: SUMMARY OUTAT Regression Statistics Multiple R 10.901667336 R square 0.813003986 Adsusted o sguaste 0.798619677 Standard erox 1.537360137 Observations 15 A NOVA df Regression I ss I MS significancer 133.5841429 133.5841429 56.52019844.385681-04 30.72519048 2.36347618 164.3093335 13 Residual Total intexcept Year coefficients Standard exal Estat P-value Lower 95% uppe895) 42.9809523801835337183 51-453416992.06998E-16141.17631614 44.7855896 10.690714286 0.091874847.5179916374138568E-6 0.49223675 0.889197814 * Percentage of adults who exercise 30 of more minutes at least three times per weer=0169071 Year + 42.98095

Normal Calculations:- Sum of x=120 Sum of y=727.6 Meanx=8 Meany = 48.5067 Sum of squares (55x)=280 Sum of products (SP) = 193.4 Regression equation = ý=bx+a b=sp/Ssx = 19314/280 -0.6907) a = My-bMx=48151 -(0.69*8) = 42198095 Û =0.690714+4298095 Iyear percentage of adults who exercise 3060) Moremin at least X-My Y-My CX-M three times. T. 418 2 45.4 3. 47.2 4. 45.7 5. 46.8 6. 44.8 7. 47.8 8. 50.5 9. 48.3 |-6,7067 49 1-3, 1067 36 -1.3067.25 -2.8067 16 -1.70679 - 7067 4 -0220671 199330 -0.2067 0.7933.4 0.99339 31993316 2.1933 | 25 6.493336 10. 49.3 11. 495 12. 52,5 13. 50.7 14. 55. 15. 52.3 3.7933 49

35:280 y =0.69071x + 42.98095 . c) at ye at year = 16 means x=16 =0.69071 * 16 +42198095 -54.0323 * In year 16, 54.03% of adults will report that they exercise F08 30608) more minutes at least three times per week, d) at year at year 18 means x=18 8 = 0. 6 p|x 18+ 42:48045-55: 4131 * In yeare 18, 55,41% of adults will report that they eaercise for 306030 more minutes at least three times per week.