Year Advertising Expenditure $ 000 Membership Subscriptions 2013 51 62 2014 58 68 2015 62 66 2016 65 66 2017 68 67 2018 76 72 2019 77 73 2020 78 72 2021 78 78 2022 84 73 2023 85 76 (i) Plot the scattergraph for the data. (ii) Use the data, to develop a regression equation relating advertising expenditure to membership. (iii) Estimate the membership if $40 000 is spent on advertising. (iv) How much must be spent on advertising to obtain a membership of 80 (000)? (v) What is the nature of the relationship between advertising expenditure and membership? (vi) Forecast 2024 membership using an alternative method, clearly explaining the limitations of your selected method. (vii) What are the limitations of the method used in (iii)?
|
Year |
Advertising Expenditure |
Membership Subscriptions |
|
2013 |
51 |
62 |
|
2014 |
58 |
68 |
|
2015 |
62 |
66 |
|
2016 |
65 |
66 |
|
2017 |
68 |
67 |
|
2018 |
76 |
72 |
|
2019 |
77 |
73 |
|
2020 |
78 |
72 |
|
2021 |
78 |
78 |
|
2022 |
84 |
73 |
|
2023 |
85 |
76 |
(i) Plot the scattergraph for the data.
(ii) Use the data, to develop a regression equation relating advertising expenditure to membership.
(iii) Estimate the membership if $40 000 is spent on advertising.
(iv) How much must be spent on advertising to obtain a membership of 80 (000)?
(v) What is the nature of the relationship between advertising expenditure and membership?
(vi) Forecast 2024 membership using an alternative method, clearly explaining the limitations of your selected method.
(vii) What are the limitations of the method used in (iii)?
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