The relationship between income and happiness has been studied extensively, both on an individual and on a societal level. Worksheet Happiness contains data about annual gross income (in thousands of dollars) and a life satisfaction score (measured on a 100-point scale) for 50 individuals.

1. Look a scatterplot relating life satisfaction on the y-axis to income on the x-axis. What does this scatterplot tell you about the relationship between these two variables?

2. Fit a second-order polynomial model (with income and the square of income as the independent variables) to predict life satisfaction. How well does this model fit the data?

3. Using your model from part b), what change in the life satisfaction score would you expect if income increases from $60,000 to $70,000?

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4. Using your model from part b), what change in the life satisfaction score would you expect if income increases from $160,000 to $170,000? Why is this answer different from the one in part c) and does this difference make sense given what you saw in the data in part a)?

5. Another way to model this data set is to distinguish between low income and high income people and let the impact of income on life satisfaction depend on which income group a person belongs to. So, create a model that divides the 50 people into two groups: those below the median income and those above the median income. Create a variable that distinguishes between these two groups and also let the impact of income on life satisfaction depend on which particular group a person belongs to. Carefully explain how you build this model and interpret how this model works (in particular how the individual slopes impact predictions of life satisfaction based on incom.

6. Using your model from part e), what change in the life satisfaction score would you expect if income increases from $60,000 to $70,000?

7. Using your model from part e), what change in the life satisfaction score would you expect if income increases from $160,000 to $170,000? Why is this answer different from the one in part f)?

Please use excel, Thank you Life Satisfaction 29 36 30 31 36 36 43 28 42 1 Income (in thousands of dollars) 2 58 3 60 4 63 5 64 6 69 7 69 8 73 9 77 10 92 11 87 12 88 13 99 14 97 15 100 16 102 17 106 18 110 19 117 20 120 21 125 22 127 23 137 24 139 25 141 26 142 27 144 28 150 29 156 30 156 31 158 32 158 158 34 160 35 162 36 164 37 168 38 170 39 171 40 172 41 172 42 173 43 173 44 174 45 177 46 180 47 190 48 194 49 194 50 200 51 200 52 42 51 48 61 51 52 61 54 56 53 58 59 67 69 61 63 73 62 70 65 63 72 68 69 65 69 75 67 72 76 69 57 59 70 62 79 64 69 75 59 69 Life Satisfaction 29 36 30 31 36 36 43 28 42 1 Income (in thousands of dollars) 2 58 3 60 4 63 5 64 6 69 7 69 8 73 9 77 10 92 11 87 12 88 13 99 14 97 15 100 16 102 17 106 18 110 19 117 20 120 21 125 22 127 23 137 24 139 25 141 26 142 27 144 28 150 29 156 30 156 31 158 32 158 158 34 160 35 162 36 164 37 168 38 170 39 171 40 172 41 172 42 173 43 173 44 174 45 177 46 180 47 190 48 194 49 194 50 200 51 200 52 42 51 48 61 51 52 61 54 56 53 58 59 67 69 61 63 73 62 70 65 63 72 68 69 65 69 75 67 72 76 69 57 59 70 62 79 64 69 75 59 69