In Problem 14.4 on page 583, you used sales and number of...

In Problem 14.4 on page 583, you used sales and number of orders to predict distribution costs at a mail-order catalog business (stored in WareCost). Use the results from that problem. a. Construct a $95 \%$ confidence interval estimate of the population slope between distribution cost and sales. b. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.

In Problem 14.4 on page 583, you used sales and number of orders to predict distribution costs at a mail-order catalog business (stored in WareCost). Use the results from that problem.
a. Construct a $95 \%$ confidence interval estimate of the population slope between distribution cost and sales.
b. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.

Key Concepts

Confidence Interval for a Regression Coefficient

This concept refers to the range of values, constructed around an estimated regression coefficient, within which the true population parameter is expected to lie with a specified degree of confidence (e.g., 95%). It involves using the estimated coefficient, its standard error, and the critical value from the t-distribution based on the desired confidence level.

t-Distribution in Regression Analysis

The t-distribution is used when the sample size is relatively small or when the population standard deviation is unknown. In regression analysis, it allows for the construction of confidence intervals and the performance of hypothesis tests by accounting for additional uncertainty in the estimation of regression coefficients.

Hypothesis Testing for Regression Coefficients

This involves testing if an individual regression coefficient is significantly different from zero. By setting up a null hypothesis (that the coefficient equals zero) and an alternative hypothesis (that it does not), one can use the t-statistic and corresponding p-value to assess whether the independent variable contributes significantly to the model.

p-Value and Significance Level

The p-value indicates the probability that the observed data would occur if the null hypothesis were true. When compared to a predetermined significance level (such as 0.05), it helps decide whether to reject the null hypothesis. A p-value lower than the significance level signals that the variable is significantly associated with the dependent variable.

Regression Model Selection

This key concept involves choosing the appropriate predictor variables to include in the regression model based on their statistical significance and contribution to explaining the variation in the response variable. It aims to create a model that is both efficient and interpretable by excluding variables that do not provide meaningful explanatory power.

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