Arithmetic Mean and Life Satisfaction

PART A: i) Male: Female: The mean value of life satisfaction for male is about 7. 7459 while for female is 7. 7101, which proves there is no significant different life satisfaction between male and female, thus gender does not affect life satisfaction a lot. But when it comes to sample variance, for male is 2. 5684 while for female is 3. 0081. From this pair of figures it is obvious that the life satisfaction for female is more flexible than male. Man’s life satisfactions are easy to be affected by other variables. I assume “GENDER” does not affect life satisfaction. ii) Not alone: Alone:

The mean value of satisfaction for those who is not alone is about 7. 8055 meanwhile the figure for those who live alone is 7. 32584. There is a big gap between these two data, which implies that “ALONE” have a significant impact on people life satisfaction. Additionally, sample variance for alone is much higher than for not alone, which implies other variables affect people who live alone severely and affect people not alone a little. I assume “ALONE” affects “LIFESAT” vitally, since people feel happier when they are accompanied by others but for those who are alone are easy to feel lonely and sad. iii) Income 1: Income 6:

The average life satisfaction for people with income level 1 is 7. 4426 while for people with income level 6 is 8. 2069, which means people with high income are more satisfy with their life than those with low income. Furthermore, the sample variance for income 1 is 4. 37941 while for level 6 is only 0. 74138, which tells that people with relatively 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 capable to purchase what they like which makes people satisfy with their lives. PART B: i) Y=7. 746-0. 036X (gender)

For gender, the ? 2 is -0. 036 which means gender has negative 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 result is not exactly what I have supposed. My prior assumption is ? 2 should be zero 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 satisfied with their life. ?2 is a little bit different 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 might be easy to feel satisfied about life. For young people they are more likely to be ambitious and do not feel enough 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 have less life satisfaction than those accompanied by others. The result is in accordance 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 will 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. PART 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 religion as another independent variable, “0” represents no religion and “1” means having religion.

In my opinion, when other variables remains stable people with religion compared with people without religion are more satisfied with their lives, since people with religion have spiritual sustenance. Hours spend on sleep every week can also 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 calculated in part c: Yhat=6. 4981-0. 0094X1-0. 0005X2+0. 0497X3+0. 0170X4-0. 3975X5+0. 1986X6 SSE=(Y-YHAT)^2 One example for made up coefficients: As I change the portfolio of coefficient, the new sum of squared residuals ever lower than the original SSE. The coefficients we got by applying the OLS model contributes to the most minor sum of squared residuals. PART G: i) H0: ? 1=0 H1: ? 1? 0 Test 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| Reject H0 at 10%, 5%, and 1% level of significant. Therefore ? 1 is significant different from 0 at all these three level. ii) H0: ? 2=0 H1: ? 2? 0 Test statistic:

T=(-0. 0094153888009149-0)/ 0. 00475949120927804= -1. 97823430844052 |t|=|-1. 97823430844052|=1. 97823430844052 |t0. 95, 1653|<|t0. 975, 1653|<|t|<|t0. 95, 1653| Hence, the null hypothesis is not rejected at 1% level of significant, but rejects H0 at 10% and 5%. Therefore, ? 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. 593905372042513<|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 model: 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).