Regression for Cost Estimation: Read R², Coefficients & Excel Output

Read regression output to estimate overhead costs from activity drivers. Professor Farhat compares regression with the high-low method, interprets an Excel-style output table, and introduces multiple regression using labor hours and material cost. For cost and managerial accounting students, CMA candidates and CPA candidates reviewing cost estimation. This lesson interprets results; it does not demonstrate the Excel setup clicks. Read the statistical clarifications below alongside the recording. Study resources: https://farhatlectures.com THE COST MODEL Estimated total cost = a + bX. The intercept a estimates the fixed component; slope b estimates cost per unit of the selected driver, if that interpretation fits the business and data. The lecture’s rounded single-driver equation is approximately: Estimated overhead = $20,378 + $34.64 × labor hours. Least squares fits the observations by minimizing squared residuals; the fitted line need not pass through every point. High-low instead uses the highest and lowest activity observations. CHAPTERS 00:00 Regression for cost estimation 00:46 High-low method versus regression 02:14 JK Renovation: labor hours and overhead 02:56 Multiple R discussion 04:10 R-squared and explained variation 05:27 Regression standard error and observations 06:03 Intercept: estimated fixed component 06:41 Labor-hour slope coefficient 06:59 Build the estimated cost equation 07:46 What a zero slope means in the model 08:13 t-statistic discussion 08:51 p-value discussion 09:49 Confidence-interval discussion 11:10 Adding another cost predictor 12:14 Multiple regression: labor hours and materials 13:04 Comparing model fit 14:05 Data quality and model limitations 14:43 Investigating influential outliers 16:25 Inflation and matching time periods 16:46 Study resources STATISTICAL CLARIFICATIONS • 02:56: For ordinary Excel regression with an intercept, Multiple R is the nonnegative square root of R². It is not the signed Pearson correlation, which can range from −1 to +1. A near-zero linear correlation does not rule out a nonlinear relationship. • 04:10: R² of about 0.733 means the fitted model explains about 73.3% of the sample variation in overhead around its mean. It does not mean labor causes 73.3% of overhead dollars, nor guarantee forecast accuracy. Correlation alone does not establish causation. • 05:27–07:58: Residual standard error describes unexplained scatter in cost units and matters for uncertainty. The intercept at zero activity can be outside the observed range; it is not automatically a verified cost at shutdown. A zero estimated slope means no fitted linear change for that driver, not proof that all real costs are fixed. • 08:13: A t-statistic is not the slope. For a zero-coefficient null hypothesis, t = estimated coefficient ÷ that coefficient’s standard error. Evaluate a two-sided test using |t|, degrees of freedom and the chosen significance level; “greater than 2” is only a rough shortcut. • 08:51: A p-value measures how unusual the observed test statistic or a more extreme result would be under the null model and its assumptions. It is not the probability that the relationship is coincidence or that the null is true. Small p-values do not by themselves establish practical importance. • 09:49: A usual 95% coefficient confidence interval is estimate ± t-critical × standard error, not estimate ± one standard error. The procedure has 95% long-run coverage under its assumptions. It does not say the estimated cost is 95% certain to be correct or define the relevant activity range. • 11:10–14:05: Adding predictors to the same ordinary least-squares sample cannot lower unadjusted R², but can worsen prediction. Consider adjusted R², residual patterns, business reasoning and validation on new data. Do not automatically discard adjusted R². • 14:43: Investigate unusual observations and document any exclusion. Removing an outlier does not guarantee the “true” cost line. Correct errors and assess whether unusual but valid observations belong in the intended model. STUDY CHECK Identify the response, driver units and sample period; read coefficients and uncertainty; check data quality and plausible cost behavior before forecasting. Avoid extrapolating beyond a supported activity range. CONTINUE STUDYING Cost Estimation: High-Low & Regression:    • Cost Estimation: High-Low & Regression | C...   REFERENCES Microsoft LINEST documentation: https://support.microsoft.com/en-us/e... Penn State: regression coefficient tests and intervals: https://online.stat.psu.edu/stat501/L... Penn State: model building and adjusted R²: https://online.stat.psu.edu/stat501/L... American Statistical Association: p-value guidance: https://www.amstat.org/asa/files/pdfs... #RegressionAnalysis #CostAccounting #CMAExam