Exploring Scatter Plots and Correlation Analysis

What is the primary purpose of a scatter plot?

• To predict future trends with 100% accuracy

• To create a perfect linear relationship between variables

• To display data visually and observe relationships between variables

• To calculate the exact value of data points

What happens to snow cone sales as the temperature increases?

• Sales decrease

• Sales remain constant

• Sales increase

• There is no clear pattern

What does a positive correlation indicate?

• The variables are unrelated but have a constant difference

• There is no relationship between the variables

• As one variable increases, the other also increases

• As one variable increases, the other decreases

What does a negative correlation imply?

• As one variable increases, the other also increases

• The variables are completely unrelated

• As one variable increases, the other decreases

• There is no relationship between the variables

What indicates no correlation between two sets of data?

• All data points lying on the line of best fit

• A positive slope on the graph

• Data points scattered randomly without any pattern

• A perfect linear relationship

What is a line of best fit?

• A line that perfectly passes through all data points

• A line that divides the graph into two equal halves

• A line that has as many points above it as below it, going through the center of the data

• A line that predicts future data points with absolute certainty

How can trend lines be used?

• To make predictions based on the data

• To draw perfect circles

• To calculate the area under the curve

• To separate data points clearly

What is interpolation?

• Ignoring the data points and guessing the outcome

• Making predictions based on values outside the data range

• Calculating the exact line of best fit

• Making predictions based on values within the data range

What is extrapolation?

• Predicting values within the data range

• Predicting values outside the data range

• Drawing a line of best fit through all data points

• Calculating the mean of the data points

Why must one be cautious when extrapolating?

• It always results in a negative correlation

• Predictions can often be misleading

• It can lead to overfitting the model

• It is not allowed in statistical analysis