8.SP.2

Explain why straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Example Problems
A fishery biologist recorded the length of trout, in centimeters, and their weight, in grams.
After plotting her results, the biologist noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following
least squares regression equation for predicting weight, in grams, from length, in centimeters:



What is the
residual for a trout that is long and weighs ?
A mobile carrier recorded each customer's monthly data usage, in GB, and their monthly bill, in dollars.

After plotting their results, the analysts noticed that the relationship between the two variables was fairly linear, so they used the data to calculate the following
least squares regression equation for predicting the monthly bill, in dollars, from data usage, in GB:



What is the
residual for a customer who used and was billed ?
A fitness trainer recorded the number of steps a client took in a day and the calories burned, in calories.

After plotting her results, the trainer noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following
least squares regression equation for predicting calories burned from steps taken:



What is the
residual for a day with 8000 steps and 560 calories burned?
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