MATH225N Week 8: Predictions Using Linear Regression

Description

MATH225N Week 8: Predictions Using Linear Regression

Question

The table shows data collected on the relationship between age (in years) and daily time spent on the phone. The line of best fit for the data is yˆ=−0.68x+95.6. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

Age (Years) 30405060 Minutes on the Phone 75696155

(a) According to the line of best fit, what would be the predicted number of daily minutes spent on the phone for a person who is 27 years old? Round your answer to two decimal places.

Correct answer:

The predicted number of daily minutes spent on the phone is 77.24.

Question

The table shows data collected on the relationship between age (in years) and daily time spent on the phone. The line of best fit for the data is yˆ=−0.68x+95.6.

Age (Years) 30405060 Minutes on the Phone 75696155

(a) According to the line of best fit, the predicted number of daily minutes spent on the phone for a person who is 27 years old is 77.24.

Correct answer:

The estimate, a predicted time of  77.24 minutes, is unreliable but reasonable.

(b) Is it reasonable to use this line of best fit to make the above prediction?

SOLUTION:

Predictions Using Linear Regression (with citations)

1) Context and model

You’re studying the relationship between age (years) and daily minutes on the phone. The observed pairs (ages 30, 40, 50, 60 with minutes 75, 69, 61, 55) display a downward trend: older individuals tend to spend fewer minutes on the phone per day. A least-squares regression has been fit and deemed significant with a strong linear relationship:

y^=−0.68x+95.6,\hat{y} = -0.68x + 95.6,y^​=−0.68x+95.6,

where $x$ is age and y^\hat{y}y^​ is predicted daily minutes on the phone. Interpreting a fitted line involves reading the slope and intercept in context, while remembering that the intercept may not be intrinsically meaningful if $x=0$ lies far outside the observed range (Triola, 2018; Sullivan, 2019).………………………………..Get a complete solution at $ 9.9