1. a) When does it make sense to choose a linear function to model a set of data?
If the data for a graph or data table is not linear and you want to find the rate of change, it would make sense to use a linear function for that because although everyone is going to get a different equation as long as you get two points on the line of best fit, then it will work with the equation, but it has to be on the trend line. That way you can make predictions to find values that aren't on the graph. As well of course when there is linear data or somewhat linear data.
b) What steps would you follow to find a line of best fit? Include how you would calculate the residuals and what those results might tell you.
To find the line of best fit, I would just try to make a line where it goes as closest to all of the points to minimize the residual values. To calculate the residuals you take the actual data point and the theoretical or model point. The smaller the residual is, the more accurate the line of best fit is.
If the data for a graph or data table is not linear and you want to find the rate of change, it would make sense to use a linear function for that because although everyone is going to get a different equation as long as you get two points on the line of best fit, then it will work with the equation, but it has to be on the trend line. That way you can make predictions to find values that aren't on the graph. As well of course when there is linear data or somewhat linear data.
b) What steps would you follow to find a line of best fit? Include how you would calculate the residuals and what those results might tell you.
To find the line of best fit, I would just try to make a line where it goes as closest to all of the points to minimize the residual values. To calculate the residuals you take the actual data point and the theoretical or model point. The smaller the residual is, the more accurate the line of best fit is.
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