Question

Does the function you chose seem appropriate? In other words, does the model line match your data well? Yes or no. Explain your basis for deciding whether or not it matches well.

Answer 1

To decide if a model line matches the data, examine the overall trend, check for outliers, and consider the strength of correlation. The least-squares method helps quantify the fit, and the slope indicates the relationship between variables.

Step-by-step explanation:

To assess whether a function or model line matches data well, consider several key points. A line fits the data well if it captures the overall trend of the data points without too many deviations. A good fit would generally have data points scattered evenly around the line, with no clear patterns left unexplained. Correlation is also important in determining the fit; a higher correlation indicates a stronger linear relationship.

Regarding outliers, you need to identify any data points that are significantly different from others. Outliers can markedly affect the fit of a model. If an outlier is a result of a measurement error or other anomaly, it may be appropriate to remove it, but if it's a valid observation, it should be included in the analysis.

Finally, the fit of a line can be quantitatively evaluated using the least-squares method, which minimizes the sum of the squares of residuals (differences between the observed values and those predicted by the model). The slope of this line offers insights into the relationship between the variables. For example, a positive slope indicates that as one variable increases, the other variable tends to increase as well.