Question

Statistics Problem:

You have been asked to engage in one final project for the political organization for which you have been working. This time you wish to study the nature of the relationship between the ages of the donors to the campaign and the amount of money they plan to donate or have donated. Data is collected from a random sample of supporters of the candidate. This data is shown on the next page. Various questions need to be answered about the results you generate. These questions follow the presentation of the data. You should answer the questions posed in the narrative that should accompany your results.

Data:

                        Age of Supporter                              Donation

                                    22                                            $   75

                                    38                                               135

                                    50                                               100

                                    46                                                 50

                                    60                                               200

                                    28                                                   0

                                    25                                                 10

                                    69                                                 35

                                    75                                                 75

                                    28                                               100

                                    55                                               250

                                    37                                               100

                                    36                                               100

                                    43                                               125

                                    35                                                   0

                                    19                                                   0

                                    48                                                 50

                                    70                                                 25

                                    31                                               115

                                    30                                               105

Part 1 Questions:

a)        Create a scatter diagram of this data. Before you proceed further, make some observations about the behavior of the data, if you are able, based solely upon this diagram.

b)        Find the regression coefficients and the regression equation for this data by using the method of least squares analysis.

c)         On a separate scatter diagram, plot the regression line. State any additional observations about the behavior of the data you can make because of your new scatter diagram.

d)        Provide meanings for each of the regression coefficients. Be sure these meanings relate specifically to the problem you are studying

e)        Use your regression equation in order to predict the donation for a supporter who is 30 years old. Do the same for a supporter who is 80 years old. Do you have any concerns with either of these predictions? State a reason or reasons for any concerns you might have.

f)          Find the sample coefficient of determination for the above data. Explain its meaning relative to the problem.

g)        Find the adjusted sample coefficient of determination for the above data. Explain its meaning relative to the problem. Why does it differ, if it does, from the coefficient of determination that you found in the previous part of the problem?

Answer 1

Solution:

Here we solve this problem using minitab software

a) Create a scatter diagram of this data. Before you proceed further, make some observations about the behavior of the data, if you are able, based solely upon this diagram

Ans:

Comment : Here using the scatter plot we say that there is week positive correlation between age of supporter and Donation

b)        Find the regression coefficients and the regression equation for this data by using the method of least squares analysis.

Regression Equation:

Donation = 44.0 + 0.911 Age of supporter

regression coefficients

0 =44.0 and 1 = 0.911

c)  On a separate scatter diagram, plot the regression line. State any additional observations about the behavior of the data you can make because of your new scatter diagram

Comment : In the above the graph we say that spread of the data is outward funnel it means that we say that there is no constant mean and variance i.e variance is increase (outward funnel)

d) Provide meanings for each of the regression coefficients. Be sure these meanings relate specifically to the problem you are studying

Ans:0 =44.0 is the intercept of Y axis in this problem if the value of age of supporter is zero then Donation value is 44.0

and

1 = 0.911

The slope of a regression line represents the rate of change in y as x changes. Because y is dependent on x, the slope describes the predicted values of y given x.

where x is age of supporter and Y is Donation.

e)        Use your regression equation in order to predict the donation for a supporter who is 30 years old. Do the same for a supporter who is 80 years old. Do you have any concerns with either of these predictions? State a reason or reasons for any concerns you might have.

Ans :

i)

Donation for a supporter who is 30 years old.

Donation = 44.0 + 0.911 Age of supporter.

Donation = 44.0 + 0.911 * (30)

Donation = 44.0 + 27.33

Donation = 71.33

ii)

Donation for a supporter who is 80 years old

Donation = 44.0 + 0.911 * (80)

Donation = 44.0 + 72.88

Donation = 116.88

f) Find the sample coefficient of determination for the above data. Explain its meaning relative to the problem.

coefficient of determination for the above data is R-Sq = 5.2%

g)

adjusted sample coefficient of determination for the above data. is R-Sq(adj) = 0.0%

Thank You..!!

please like it..