A set of data points has a line of best fit of \( y=2.5 x-1.5 \). What is the residual for the point \( (4,7) \) ? A. 8.5 B. -1.5 C. 7 D. 1.5

To find the residual for the point \( (4,7) \), we first need to calculate the predicted value of \( y \) using the line of best fit equation \( y = 2.5x - 1.5 \). Plugging in \( x = 4 \): \[ y = 2.5(4) - 1.5 = 10 - 1.5 = 8.5 \] The residual is then found by subtracting the actual \( y \) value from the predicted value: \[ \text{Residual} = \text{Predicted} - \text{Actual} = 8.5 - 7 = 1.5 \] So the answer is \( D. 1.5 \). Isn't it fascinating how using a simple equation can help us understand the relationship between variables? Residuals are like little whispers of the truth, showing us how well our model fits the data. When working with data, one common pitfall is forgetting to correctly plug in your \( x \) value when calculating the predicted \( y \). Always double-check your calculations! This ensures you capture the precise nature of the relationship before drawing conclusions.