The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.
|
Year (x) |
Rural Household (y%) |
Urban Household (y%) |
|
2020 |
2 |
6 |
|
2021 |
3 |
7 |
|
2022 |
3 |
9 |
|
2023 |
4 |
15 |
|
2024 |
5 |
20 |
Based on the above data, which of the following statements are correct?
(A) A straight line trend by the method of the least squares for rural Indians is $y_t = 3.4 + 0.7$ (x - 2022)
(B) A straight line trend by the method of the least squares for urban Indians is $y_t = 11.4 + 4.3$ (x - 2022)
(C) The forecast for the year 2025 for urban group using the trend equation is 22.2%.
(D) The forecast for the year 2025 for rural group using the trend equation is 5.5%.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C) and (D) only
Data: $x\in\{2020,2021,2022,2023,2024\}$, let $t=x-2022\in\{-2,-1,0,1,2\}$.
Rural $y$: $[2,3,3,4,5]$
Fit $y=a+bt$ by least squares. Computation gives
$a=3.4,\;b=0.7$
Trend for rural: $y_{t}=3.4+0.7(x-2022)$
Urban $y$: $[6,7,9,15,20]$
Fit $y=a+bt$ by least squares. Computation gives
$a=11.4,\;b=3.6$
Trend for urban: $y_{t}=11.4+3.6(x-2022)$
Forecast for 2025 ($x-2022=3$):
Rural: $y_{2025}=3.4+0.7(3)=5.5\%$
Urban: $y_{2025}=11.4+3.6(3)=22.2\%$
Correct options
(A) True
(B) False
(C) True
(D) True