Notes 3.3: Least Squares Regression Line
Learning Target Least Squares Regression Line LSRL (Least Squares Regression Line aka Line of Best Fit): The line of best fit that ALWAYS passes through the point ( x? , y? ). What makes a LSRL a “good” line of best fit???Example 1: Which line is the “correct” LSRL for the data given that ( x? , y? ) = (1955, 17583)? Justify your decision.137160014922500Note: It is possible to have all, few, or none of the data points on the line of best fit.An LSRL has the general form of: LSRL = y? = slope x + y-intercepty-hat (y?): Represents the predicted y value based on the LSRL. It is NOT an actual data point, but predicted based on the equation.Slope: A number that describes both the direction and steepness of a line.y-intercept: The value of y where the LSRL crosses the y-axis.We will always write a LSRL symbolically using the general form and in context using words. We will use technology to determine the slope and y-intercept in order to write an equation for the line of best fit.? I can calculate and interpret the slope of a line of best fit using correlation ?We can use a calculator to determine the slope of a line of best fit.Step 1: Turn Diagnostics on. Press 2nd CATALOG, scroll to DiagnosticOn, and press ENTER twice.Step 2: Enter data into L1 and L2.Step 3: Press STAT and scroll right to CALC. Scroll to 4: LinReg(ax+b) and press ENTER.Step 4: Make sure L1 is listed next to Xlist, L2 is listed next to Ylist. Scroll down to Calculate and press ENTER.224980566675001419225977900 Slope36576005651500Example 2: Use a calculator to find the slope for a LSRL based on the data for fat and calories.Slope = a = __________Interpretation of slope in terms of context: As fat increases by 1 gram, calories increase by _______________.? I can calculate and interpret the y-intercept of a line of best fit ?We can use a calculator to determine the y-intercept of a line of best fit.Step 1: Turn Diagnostics on. Press 2nd CATALOG, scroll to DiagnosticOn, and press ENTER twice.Step 2: Enter data into L1 and L2.Step 3: Press STAT and scroll right to CALC. Scroll to 4: LinReg(ax+b) and press ENTER.Step 4: Make sure L1 is listed next to Xlist, L2 is listed next to Ylist. Scroll down to Calculate and press ENTER.224980566675001419225406400 y-interceptExample 3: Use a calculator to find the slope for a LSRL based on the data for fat and calories.y intercept = b = __________Interpretation in terms of context: When x = 0 (no fat grams), the calorie content is ______________.? I can determine the equation for a line of best fit (LSRL) ?Once you have calculated slope and y-intercept, you can write the equation for the LSRL. Be sure to write the LSRL symbolically using the general form and within context using words.Example 4: Find the LSRL for the fat and calories data. y? = slope x + y-intercept = __________________________ Predicted Calorie Content = 10.3 (Fat in Grams) + 72.7? I can use the line of best fit (LSRL) to make predictions ?Example 5: Using the line of best fit you determined in Example 4 for the fat and calories data, estimate the predicted calorie content for a piece of meat with 5 grams of fat. ................
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