Final answer:
To predict etching rate from room temperature using the least-squares regression line, enter the data into a calculator, make a scatter plot, compute the regression line equation using the form ý = a + bx, add it to the plot, and evaluate the significance of the correlation coefficient.
Step-by-step explanation:
To find the equation of the least-squares regression line for predicting etching rate from room temperature, the process involves a few steps. First, enter the data into a calculator to make a scatter plot.
Then, using the calculator's regression function, find the least-squares regression line equation. This equation will typically be in the form ý = a + bx, where ‘a’ is the y-intercept and ‘b’ is the slope of the line.
After computing this, you can add the regression line to your scatter plot from the initial step to visualize the predictive relationship between the variables.
To further analyze the strength of the relationship, calculate the correlation coefficient. If the correlation coefficient is close to 1 or -1, it implies a significant relationship between the variables, while a coefficient close to 0 implies a weak relationship.
For practical application, once you have the regression line equation, you can use it to make predictions. For example, given the room temperature, you can plug it into the equation to predict the etching rate.
Be mindful that predictions are reliable within the range of data from which the regression model was developed and may not be accurate for extrapolated values far outside the original data range.