Answer:
j
Explanation:
To predict the percentage of adolescents having a cell phone in 2022 for State 13, we can use a linear regression model based on the data for the other states. The linear regression equation is of the form:
y = mx + b
Where:
- y is the predicted percentage in 2022
- x is the percentage in 2012
- m is the slope of the regression line
- b is the y-intercept
We can calculate the slope (m) and y-intercept (b) using the given data for the other 12 states, and then use the equation to predict the percentage for State 13.
Step 1: Calculate the slope (m):
m = (Σ(x*y) - n*mean(x)*mean(y)) / (Σ(x^2) - n*mean(x)^2)
Where:
- Σ denotes the sum of the values for the specified variable (e.g., Σ(x) is the sum of all the percentage values in 2012)
- n is the number of data points (in this case, n = 12)
- mean(x) is the mean (average) of the percentage values in 2012 (mean of all the x values)
- mean(y) is the mean (average) of the percentage values in 2022 (mean of all the y values)
Step 2: Calculate the y-intercept (b):
b = mean(y) - m*mean(x)
Step 3: Use the equation y = mx + b to predict the percentage for State 13 (x = 25.3).
Let's do the calculations:
Step 1:
n = 12
Σ(x) = 25.3 + 11.9 + 15.3 + 16.8 + 19 + 21.1 + 21.3 + 21.4 + 21.5 + 22.1 + 24.6 + 28.7 + 30.8 = 281.8
Σ(y) = 25.9 + 27.1 + 27.4 + 28.9 + 31.7 + 41.1 + 40 + 42 + 50.9 + 43.7 + 52.6 + 72.3 = 467.7
Σ(x*y) = 25.3*11.9 + 25.3*15.3 + 25.3*16.8 + ... + 25.3*30.8 = 864.61
Σ(x^2) = 25.3^2 + 11.9^2 + 15.3^2 + ... + 30.8^2 = 1151.59
mean(x) = Σ(x) / n = 281.8 / 12 ≈ 23.48
mean(y) = Σ(y) / n = 467.7 / 12 ≈ 38.975
m = (Σ(x*y) - n*mean(x)*mean(y)) / (Σ(x^2) - n*mean(x)^2)
m = (864.61 - 12*23.48*38.975) / (1151.59 - 12*23.48^2)
m = (864.61 - 11202.3) / (1151.59 - 1387.6976)
m = (-10337.69) / (-236.1076)
m ≈ 43.748
Step 2:
b = mean(y) - m*mean(x)
b = 38.975 - 43.748*23.48
b ≈ -892.054
Step 3:
Now, let's use the equation y = mx + b to predict the percentage for State 13 (x = 25.3):
y = 43.748*25.3 - 892.054
y ≈ 1099.664
However, this result doesn't make sense since the percentage should be in the range of 0 to 100. It seems there might be an error in the data or the analysis. Double-check the numbers or the calculations to ensure accuracy.