Arithmetic Mean and Life Satisfaction

neighborhood A i) Male Fe masculine The misbegot apprize of livelihood propitiation for male is about 7. 7459 speckle for effeminate is 7. 7101, which proves thither is no evidential assorted purport satisfaction between male and female, thusly gender does non come upon spirit satisfaction a lot. But when it comes to sample variance, for male is 2. 5684 period for female is 3. 0081. From this rival of opines it is obvious that the living satisfaction for female is much flexible than male. Mans aliveness satisfactions be easy to be strickleed by an other(a)(prenominal) variables. I assume GENDER does not affect life satisfaction. ii) Not whole unsocialThe mean value of satisfaction for those who is not un accompanied is about 7. 8055 meanwhile the figure for those who live alone is 7. 32584. There is a big gap between these ii data, which implies that solely withdraw a substantial impact on lot life satisfaction. Addition tot exclusivelyyy, sample varia nce for alone is a lot higher than for not alone, which implies other variables affect plurality who live alone naughtily and affect people not alone a little. I assume ALONE affects LIFESAT vitally, since people feel happier when they be at moveed by others merely for those who are alone are easy to feel sole(a) and sad. iii) Income 1 Income 6The average life satisfaction for people with income level 1 is 7. 4426 while for people with income level 6 is 8. 2069, which message people with high income are much satisfy with their life than those with pathetic income. Furtherto a greater extent, the sample variance for income 1 is 4. 37941 while for level 6 is only 0. 74138, which tells that people with comparatively high income enjoys a relatively stable high life satisfaction. Personally, I reckon that people with high income are happier than those with low income, as they are more(prenominal) capable to purchase what they like which makes people satisfy with their lives. discontinue B i) Y=7. 746-0. 036X (gender)For gender, the ? 2 is -0. 036 which means gender has blackball relationship with satisfaction. And 0 represents male while 1 means female. Thus when other factors are the same, life satisfaction of female is slightly less than man. The turn out is not exactly what I hold in mulld. My preliminary assumption is ? 2 should be nobody in this circumstance. ii) Y=7. 360+0. 008X (age) From this function, age has a positive linear relationship with life satisfaction. As people grow old, they tend to be more genial with their life. ?2 is a little bit opposite from what I expected, as I suppose ? 2 should be a bigger positive number than it is.I reckon that as people grow old they tycoon be easy to feel satisfied about life. For young people they are more likely to be manque and do not feel abundant about what they have. iii) Y=7. 805-0. 480X (alone) Alone has a negative relationship with life satisfaction, it means people who are alone ha ve less life satisfaction than those accompanied by others. The result is in compliance with what I expected. iv) Y=7. 300+0. 174X (income) ?2 is 0. 174 which means as income increase by 1 unit life satisfaction bequeath go up by 0. 174. The more people earned the more satisfied they feel about their life.The result is correspondent with what I expected. exposit C Estimated sample regression function Yhat=6. 4981-0. 0094X1-0. 0005X2+0. 0497X3+0. 0170X4-0. 3975X5+0. 1986X6 PART D i) Y=6. 4981-0. 0094X1-0. 0005X2+0. 0497X3+0. 0170X4-0. 3975X5+0. 1986X6 =6. 4981-0. 0094*0-0. 0005*50+0. 0497*0+0. 0170*26-0. 3975*1+0. 1986*3 =7. 1134 ii) Y=6. 4981-0. 0094X1-0. 0005X2+0. 0497X3+0. 0170X4-0. 3975X5+0. 1986X6 =6. 4981-0. 0094*0-0. 0005*50+0. 0497*0+0. 0170*35-0. 3975*0+0. 1986*3 =7. 6639 PART E Setting piety as some other in babelike variable, 0 represents no religion and 1 means having religion.In my opinion, when other variables remains stable people with religion compared with peopl e without religion are more satisfied with their lives, since people with religion have spiritual sustenance. Hours spend on repose ever soy week can in addition be set as another independent variable (0? X? 168). I suppose that people who spent more time on sleep will be happier than those got less time on sleep. PART F Coefficients as figure in part c Yhat=6. 4981-0. 0094X1-0. 0005X2+0. 0497X3+0. 0170X4-0. 3975X5+0. 1986X6 south southeast=(Y-YHAT)2 One example for make up coefficients As I vary the portfolio of coefficient, the new sum of square up residuals ever lower than the original SSE. The coefficients we got by applying the OLS good example contributes to the most minor sum of squared residuals. PART G i) H0 ? 1=0 H1 ? 1? 0 audition statistic T= (6. 49806173672354-0)/ 0. 199293520416749= 32. 6054842281637 With ? =0. 1. From the t table, value of t with 10% level of significance and (n-7=1660-7=1653) d. f. , the critical value of t is tc=1. 645 With ? =0. 05. tc=1. 960 With ? =0. 01. tc=2. 576 t=32. 605> tc lour H0 at 10%, 5%, and 1% level of material. indeed ? 1 is earthshaking different from 0 at all these iii level. ii) H0 ? 2=0 H1 ? 2? 0 assay statisticT=(-0. 0094153888009149-0)/ 0. 00475949120927804= -1. 97823430844052 t=-1. 97823430844052=1. 97823430844052 t0. 95, 1653<t0. 975, 1653<t<t0. 95, 1653 Hence, the vapid theory is not jilted at 1% level of real, but rejects H0 at 10% and 5%. indeed, ? 2 is significant different from 0 at 10% and 5% level of significant but not significant from 0 at 1%. iii)H0 ? 3=0 H1 ? 3? 0 Test statistic T=(-0. 000506153379257048-0)/ 0. 00221826267938831= -0. 228175582612525 t=-0. 228175582612525= 0. 228175582612525<tc Hence, the null hypothesis is not rejected at 10%, 5% and 1%. Therefore, ? is not significant different from 0 at 10%, 5% and 1% level of significant. iv) H0 ? 4=0 H1 ? 4? 0 Test statistic T= (0. 0497380181150213-0)/ 0. 0837473787178692= 0. 593905372042513 t=0. 5939053720425 13<tc Hence, the null hypothesis is not rejected at 10%, 5% and 1%. Therefore, ? 3 is not significant different from 0 at 10%, 5% and 1% level of significant. v) H0 ? 5=0 H1 ? 5? 0 Test statistic T=( 0. 0169731847843023-0)/ 0. 00290570472445049= 5. 84133158523606 t=5. 84133158523606>tc Hence, reject H0 at 10%, 5%, 1% level of significant. Therefore ? 1 is significant different from 0 at all these 3 level. i) H0 ? 6=0 H1 ? 6? 0 Test statistic T= (-0. 397496187094307-0)/ 0. 11752515791858= -3. 38222210575277 t=-3. 38222210575277=3. 38222210575277> tc Reject H0 at 10%, 5%, and 1% level of significant. Therefore ? 1 is significant different from 0 at all these three level. vii) H0 ? 6=0 H1 ? 6? 0 Test statistic T= (0. 198587308642208-0)/ 0. 0338574782046911= 5. 86538983918457 t=5. 86538983918457> tc Reject H0 at 10%, 5%, and 1% level of significant. Therefore ? 1 is significant different from 0 at all these three level. viii) overall significance of the posture H0 ? 2=? =? 4=? 5=? 6=? 7=0 H1 at least one of the ? s non zero. Test statistic F= (4616. 46927710844-4396. 45885074034)/6/ 4396. 45885074034/ (1660-7) =13. 7867484996946 95th percentile for the F-distribution, F. 05, 6, 1653=2. 10 99th percentile for the F-distribution, F. 01, 6, 1653=2. 80 Since F=13. 7867484996946 > Fc therefore we reject the Null hypothesis. Hence, all the six variables together have significant effect on sales. In other words, the set of explanatory variables in the model can significantly explain the dependent variable (life satisfaction).