An analyst working for a telecommunications company has been asked to gauge the stress on its cellular networks due to the increasing use of smartphones. She decides to first look at the relationship between the number of minutes customers spent talking on their phones and the amount of cellular data they use. She collects a month’s worth of data on 300 customers who have smartphones with data plans. The mean monthly call time was found to be 258 minutes, and the mean amount of data consumed was found to be 530 megabytes. Based on the least squares regression line fitted to the data, it is found that for every minute increase in calling time, the data usage is expected to increase by 4.6 megabytes.

Question

An analyst working for a telecommunications company has been asked to gauge the stress on its cellular networks due to the increasing use of smartphones. She decides to first look at the relationship between the number of minutes customers spent talking on their phones and the amount of cellular data they use. She collects a month’s worth of data on 300 customers who have smartphones with data plans. The mean monthly call time was found to be 258 minutes, and the mean amount of data consumed was found to be 530 megabytes. Based on the least squares regression line fitted to the data, it is found that for every minute increase in calling time, the data usage is expected to increase by 4.6 megabytes.

x= 258
y=530
b1=4.6
bo=530-(4.6 x 258) = 530-1186.8=-656.8
y hat = -656.8 - (4.6 x 372) = -656.8 - 1711.2 = -2368
I'm getting the wrong answer

Answer 1

Whenever we work with an equation with given parameters, the first step is to define the equation in terms of the parameters.

Here we have
y_hat(x)=Ax+B
where
A=4.6
B is obtained from solving
530=4.6(258)+B
from which B=-656.8
Hence
y_hat(x)=4.6x-656.8

You have not posted the complete question, but it appears that you are looking for the data usage for call time=372.
So
y_hat(372)=4.6(372)-656.8=1054.4 Mb

Answer 2

To find the predicted data usage for a given minute increase in calling time, you need to use the formula for linear regression:

y = bo + b1 * x

where y is the dependent variable (data usage), bo is the intercept, b1 is the slope, and x is the independent variable (calling time).

Based on the given information:
x = 258 (monthly call time)
y = 530 (amount of data consumed)
b1 = 4.6 (slope)

To find the intercept (bo), we can rearrange the formula:

bo = y - b1 * x

bo = 530 - (4.6 * 258)
bo = 530 - 1186.8
bo = -656.8

Now, to predict the data usage for a minute increase in calling time, we substitute the values into the formula:

y hat = bo + b1 * (x + 1)
y hat = -656.8 + (4.6 * (258 + 1))
y hat = -656.8 + (4.6 * 259)
y hat = -656.8 + 1191.4
y hat = 534.6

Therefore, the predicted data usage for a one-minute increase in calling time is 534.6 megabytes.

Answer 3

To clarify, it seems that you are trying to calculate the predicted value of data usage (y hat) based on the given information. However, it appears that there might be some confusion in the calculations.

To calculate y hat (the predicted value of data usage) using the linear regression equation, you need to use the formula:

y hat = bo + b1 * x,

where bo is the intercept, b1 is the slope, and x is the independent variable (in this case, the call time).

In your example, you have incorrectly calculated the value of bo. The correct calculation should be:

bo = y - (b1 * x) = 530 - (4.6 * 258) = 530 - 1186.8 = -656.8.

Now, to find y hat, substitute the values into the equation:

y hat = -656.8 + (4.6 * x).

Given that x (call time) is 372 minutes, you can calculate y hat as follows:

y hat = -656.8 + (4.6 * 372) = -656.8 + 1711.2 = 1054.4.

So, the correct predicted value of data usage (y hat) for a call time of 372 minutes is 1054.4 megabytes.