Final answer:
To determine the appropriateness of a linear model for website visitors based on weeks online, one must analyze the data for consistent trends. Predictive models for sales or the stock market require an assessment of how the predicted values match actual data. Identifying outliers and deciding on their inclusion is important for accurate analysis, as is ensuring the model matches observations such as those in Weber's Law.
Step-by-step explanation:
Assessing the Appropriateness of Linear Models
To determine if Leo's claim that the number of visitors to each website can be modeled as a linear function of the number of weeks online, one would have to analyze the given data for trends and patterns. If the data shows a consistent rate of increase or decrease in visitors, then a linear model could be appropriate. However, if there is a significant fluctuation or non-linear trend, then a different model such as quadratic or exponential may be more suitable.
For example, if an electronics retailer used regression and found the model ‘ŷ = 101.32 + 2.48x’ to predict sales growth, where ŷ is in thousands of dollars and x is the day, we can predict sales for any given day by plugging in the value of x. For day 60, the predicted sales would be ŷ = 101.32 + 2.48(60), and for day 90, it would be ŷ = 101.32 + 2.48(90).
In another instance, if an economist is comparing a derived model to predict stock market outcomes with actual daily points on the index, the effectiveness of the model can be assessed by how well it matches the recorded data. Discrepancies can indicate the need for a more complex model or adjustments to the existing one.
It's important to identify any outliers as they can skew the analysis. In cases where outliers are found, one has to decide whether to include or remove them from the data set based on their potential impact on the study's results.
For hypotheses related to human perception, such as those based on Weber's Law, analysis of data must show whether the final weights or measures are proportionally the same in order to support the hypothesis.
When analyzing data and creating a linear equation, one must enter data into a calculator or computer, perform the necessary computations, and write down the linear equation with the coefficients rounded to the required decimal places.