Shoot to score A college hockey coach collected data from...

Shoot to score A college hockey coach collected data from the $2010-2011$ National Hockey League season. He hopes to convince his players that the number of shots taken has an affect on the number of goals scored. The coach performed a preliminary analysis, using the scoring statistics from 293 offensive players who play professional hockey. He predicts Goals from number of Shots (taken for the season). Discuss each of the conditions and assumptions required for him to proceed with the regression analysis. (www.nhl.com) Dependent variable is Goals R-squared $=63.4 \%$ $s=5.13$ with $293-2=291$ degrees of freedom $\begin{array}{lcccc}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-Ratio } & \text { P-Value } \\ \text { Intercept } & -1.77095 & 0.9087 & -1.9488 & 0.052 \\ \text { Shots } & 0.11938 & 0.0053 & 22.460 & <0.0001\end{array}$

Shoot to score A college hockey coach collected data from the $2010-2011$ National Hockey League season. He hopes to convince his players that the number of shots taken has an affect on the number of goals scored. The coach performed a preliminary analysis, using the scoring statistics from 293 offensive players who play professional hockey. He predicts Goals from number of Shots (taken for the season). Discuss each of the conditions and assumptions required for him to proceed with the regression analysis. (www.nhl.com)
Dependent variable is Goals R-squared $=63.4 \%$ $s=5.13$ with $293-2=291$ degrees of freedom
$\begin{array}{lcccc}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-Ratio } & \text { P-Value } \\ \text { Intercept } & -1.77095 & 0.9087 & -1.9488 & 0.052 \\ \text { Shots } & 0.11938 & 0.0053 & 22.460 & <0.0001\end{array}$

Key Concepts

Linearity

This concept refers to the assumption that there is a straight-line (linear) relationship between the independent variable and the dependent variable. In other words, the change in the dependent variable is proportional to the change in the independent variable. A violation of this condition can lead to biased or misleading estimates in the regression model.

Independence

The assumption of independence means that the observations (and hence the errors) must be independent of one another. This is crucial because autocorrelation or clustering within data could lead to underestimation of the standard errors and inflated type I error rates, thereby affecting inference.

Homoscedasticity

Homoscedasticity is the assumption that the variance of the error terms remains constant across all values of the independent variable. If the spread of the residuals changes at different levels of the independent variable, it can cause inefficient estimates and compromise the validity of hypothesis tests and confidence intervals.

Normality of Residuals

For many statistical tests associated with regression (like t-tests for coefficients), it's assumed that the residuals are normally distributed. This condition is important especially when sample sizes are small, as it underpins the reliability of the significance tests used in regression analysis.

Outliers and Influential Points

This concept involves checking for extreme values that could unduly affect the results of the regression analysis. Outliers or high-leverage points can distort model estimates and violate other assumptions, thus it is important to diagnose and address them to ensure robust regression outcomes.

Transcript

Please give Ace some feedback