Question:

A non-profit research organization conducted a study in which they collected data regarding people's incomes and level of happiness. The organization is interested in examining the relationship between people's happiness and their income, given the common assumption that more money results in more happiness. Although overall the researchers were able to determine a signiicant relationship between people's incomes and happiness score, the researchers speculate that once people have enough money to pay their expenses and build their savings, that more income will have little or no effect on their overall happiness. They collected data for those people's whose income was $70,000 per year or more; these data are shown below with Income shown in units of $10,000 and a happiness score between 0 and 10.

a. Draw a scatterplot of the data and explain what the graph indicates about the appropriateness of simple linear regression for these data.

b. Determine the estimated simple linear regression model for these data.

c. Interpret the coefficient from part b above.

d. What Is the value of coefficient of determination and what does it indicate about the simple linear regression model from part b?

e. Explain what you would conclude about the researchers' speculation that once people have enough money to pay their expenses and build their savings, that more income will have little or no effect on their overall happiness. Be sure to justify your conclusions with statistical evidence.

data : the income and score for 40 persons

Income 7.00439884 7.02551769 7.0320571 7.06279211 7.07616637 7.08158906 7.10161959 7.11158364 7.11722011 7.11947859 7.11950538 7.13675997 7.15367409 7.16187287 7.17639965 7.18090719 7.18611226 7.19440696 7.19503729 7.19640925 7.2070597 7.22519186 7.22826521 7.241313 7.24675483 7.26037414 7.29772228 7.30090272 7.31050264 7.31091603 7.34724552 7.36421338 7.4238325 7.43924761 7.44811656 7.45150065 7.46350981 7.4666532 7.47844662 7.48152138

Score 5.36244826 4.81153338 5.04017458 6.86338795 5.01057743 4.12164775 5.34835294 6.08647828 5.56254547 5.9518141 4.98198112 5.50662154 4.72098734 6.1604341 5.02995166 5.60796663 5.15159829 5.83619666 5.23170297 5.59639827 4.20947057 4.98525493 5.03400379 4.68281699 5.8901487 5.38139847 6.3842745 6.00498747 5.92334607 5.7474441 4.39662232 6.61827984 4.90968847 6.3596 5.96342209 4.10994465 4.50344538 5.96054731 4.87772554 6.19629

Match each data type given on the left with the most appropriate graphic visualization. Univariate quantitative data [ Choose ] Pie Chart Scatter plot Divariate quantitative vs. categorical data Bar Plot Side-by-aide Boxplot Sampling Distribution Time Sequence plot Divariate quantitative data Histogram Quantitative data over an interval I Choose ]SP20 MATH 202 MW 9:15a-10:55a Homework: Recommended Problems for Section 4.1 Score: 0 of 1 pt 1 of 17 (0 complete) 4.1.1 What is the difference between univariate data and bivariate data? Choose the correct answer below. O A. In univariate data, the data are qualitative, In bivariate data, the data are quantitative. O B. In univariate data, there is one mean. In bivariate data, there are two means O C. In univariate data, a single variable is measured on each individual In bivariate data, two variables are measured on each individual. O D. In univariate data, there are only positive values and zeros. In bivariate data, there are positive values, negative values, and zeros. Click to select your answer and then click Check Answer Clear All All parts showing A\fConsider the general two-state continuous-time Markov chain with transition rates Q = A 0 (a) lJ'il'rite down the backward equations. (b) Show that for any t 3 D, 1110116) + angt} = A. (e) Solve the backward equations. You may use the fact that the solution of the ordinary differential equation .r'(t) = r1226) + Mt) is :r(t) = 12(0):!\" + eat/u e_\"b(s}ds. Consider a three-state continuous-time Markov chain in which the transition rates are given by The states are labelled 1 and 2. on Q: zoo ion The states are labelled 1, 2 and 3. (a) Write down the transition matrix of the corresponding embedded Markov chain as well as the transition rates out of each of the three states. (b) Use the symmetry of Q to argue that this setting can be reduced to one with only 2 states. (:3) Use the results of Problem 1 to solve the backward equations of this 3-state Markov chain