n 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 227 minutes, and the mean amount of data consumed was found to be 510 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 4.8 megabytes. Predict the amount of data used by a customer who spends 441 minutes on the phone
Well, well, well, looks like we have an analyst trying to predict the amount of data used by a phone addict. Let me put on my clown nose and calculate this for you.
According to the regression line, we've got an increase of 4.8 megabytes for every minute of talking. So, all we need to do is some simple multiplication. 441 minutes, multiplied by 4.8 megabytes... drumroll please...
The predicted amount of data used by a customer who spends 441 minutes on the phone is 2,116.8 megabytes. Woah, that's a lot of virtual chitchat!
But hey, keep in mind that this is just a prediction. People have a way of surprising us, so your actual mileage may vary. Happy data crunching!
To predict the amount of data used by a customer who spends 441 minutes on the phone, we can use the equation of the least squares regression line.
The equation would be:
Data Usage = Intercept + Slope * Call Time
From the information given, we know that the mean monthly call time is 227 minutes, and the mean amount of data consumed is 510 megabytes.
Let's calculate the intercept and slope using the information given:
Intercept = Mean Data Usage - (Slope * Mean Call Time)
= 510 - (4.8 * 227)
= 510 - 1093.6
= -583.6
Slope = (Mean Data Usage - Intercept) / Mean Call Time
= (510 - (-583.6)) / 227
= 1093.6 / 227
= 4.822
Now that we have the intercept (-583.6) and slope (4.822), we can plug in the call time of 441 minutes into the equation to predict the data usage:
Data Usage = Intercept + Slope * Call Time
= -583.6 + (4.822 * 441)
= -583.6 + 2124.102
= 1540.502
Therefore, the predicted amount of data used by a customer who spends 441 minutes on the phone is approximately 1540.502 megabytes.
To predict the amount of data used by a customer who spends 441 minutes on the phone, we can use the least squares regression line that was fitted to the data.
The regression line essentially gives us a relationship between the independent variable (calling time) and the dependent variable (data usage). In this case, we have been given that for every minute increase in calling time, the data usage is expected to increase by 4.8 megabytes.
To find the predicted amount of data used, we can use the equation of the regression line:
Data Usage = Intercept + (Slope * Calling Time)
In this equation, the intercept represents the expected data usage when the calling time is zero, and the slope represents the rate of change in data usage with respect to calling time.
Based on the given information, the mean monthly call time is 227 minutes, and the mean amount of data consumed is 510 megabytes. We can use these values to calculate the intercept and slope of the regression line.
Intercept = Mean Data Usage - (Slope * Mean Calling Time)
= 510 - (4.8 * 227)
= 510 - 1094.4
= -584.4
Slope = 4.8
Now that we have calculated the intercept and slope, we can substitute the calling time of 441 minutes into the equation to predict the data usage.
Data Usage = -584.4 + (4.8 * 441)
= -584.4 + 2116.8
= 1532.4 megabytes
Therefore, based on the least squares regression line, the predicted amount of data used by a customer who spends 441 minutes on the phone is approximately 1532.4 megabytes.