The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

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:

(A), (C) and (D) only

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