# Multiple Regression Analysis Model Formation: Checking Significance of Independent Variables

## Use the following results:

Variable | Coefficient | Standard Error | t Statistic | p Value |

INTERCEPT | -0.02686 | 0.06905 | -0.39 | 0.7034 |

FOREIMP | 0.79116 | 0.06295 | 12.57 | 0.0000 |

MIDSOLE | 0.60484 | 0.07174 | 8.43 | 0.0000 |

**A. Construct a 95% confidence interval estimate of the population slope between durability and forefoot shock-absorbing capability**

Step 1: The formula for creating the confidence interval for the population parameter is given as follows:

{` Sample estimate ± t_{α/2}*standard error Step 2: To calculatet_{α/2}, use the Excel function TINV. Go to Formulas -> More Functions -> Statistical -> TINV `}

In the TINV dialog box, enter the probability as 0.05 and degrees of freedom as 12 (=n – 2-1)

This gives the value of t_{12,0.05} as 2.17

Step 3: Use the formula described in Step 1 to get the confidence interval for the population slope.

{` Confidence interval= 0.79116 ± (2.17*0.06295) = 0.79116 ± (0.136) = (0.655, 0.927) `}

**B. At the 0.05 level of significance, determine whether each independent variable make a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.**

{` Testing significance of the variable FOREIMP (b) Step 1: establish the null and alternate hypothesis: Null hypothesis: H_{0}: b=0 Alternate hypothesis: H_{1}:b ≠ 0 Step 2: t test will be used. α= 0.05 Step 3: Establish the decision criteria: Reject H_{0}when t_{cal}> critical value Step 4: Critical value = 2.17 (from part A above) t_{cal}= 12.57 (from the regression results given) Step 5: Since t_{cal}> critical value, we reject the null hypothesisH_{0}. Thus, the variable FOREIMP makes a significant contribution to the model Testing significance of the variable MIDSOLE (c) Step 1: Establish the null and alternate hypothesis: Null hypothesis: H_{0}: c = 0 Alternate hypothesis: H_{1}: c ≠ 0 Step 2: t test will be used. α= 0.05 Step 3: Establish the decision criteria: Reject H_{0}when t_{cal}> critical value Step 4: Critical value = 2.167 (from part A above) t_{cal}= 8.43 (from the regression results given) Step 5: Since t_{cal}> critical value, we reject the null hypothesisH_{0}. Thus, the variable MIDSOLE makes a significant contribution to the model `}

Therefore, we can conclude that both the given variable have a significant contribution to the explanatory power of the regression model. Therefore, both these variables should be included.

## Excel Econometrics Tutorials

**Multiple Regression Analysis**

**Estimation and Inference****Estimation, Inference & Prediction****Model Formation: Checking Significance of Independent Variables**

**Time Series Analysis**

**Exponential Smoothing Forecasting****Plotting Linear Trend and Forecasting****Monthly Data De-Trending, Seasonal Index & Forecasting****Linear, Exponential and Quadratic Trend****Excel Tutorial for Normal Distributions**

**Data Analysis**