Jim Frost > Quotes

“Without hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. That can be costly, either in business dollars or for your reputation as an analyst or scientist.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“How to think about problems that involve weighing information.”
― Jim Frost, Thinking Analytically: A Guide for Making Data-Driven Decisions

“The low p-values indicate that both education and IQ are statistically significant. The coefficient for IQ (4.796) indicates that each additional IQ point increases your income by an average of approximately $4.80 while controlling everything else in the model. Furthermore, the education coefficient (24.215) indicates that an additional year of education increases average earnings by $24.22 while holding the other variables constant.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“values and coefficients are they key regression output. Collectively, these statistics indicate whether the variables are statistically significant and describe the relationships between the independent variables and the dependent variable. Low p-values (typically < 0.05) indicate that the independent variable is statistically significant. Regression analysis is a form of inferential statistics. Consequently, the p-values help determine whether the relationships that you observe in your sample also exist in the larger population. The coefficients for the independent variables represent the average change in the dependent variable given a one-unit change in the independent variable (IV) while controlling the other IVs.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“If your sample contains sufficient evidence, you can reject the null and favor the alternative hypothesis.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“Regression analysis mathematically describes the relationships between independent variables and a dependent variable. Use regression for two primary goals: To understand the relationships between these variables. How do changes in the independent variables relate to changes in the dependent variable? To predict the dependent variable by entering values for the independent variables into the regression equation.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“Additionally, if you take RSS / TSS, you’ll obtain the percentage of the variability of the dependent variable around its mean that your model explains. This statistic is R-squared!”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“The result is that an individual outlier can exert a strong influence over the entire model and, by itself, dramatically change the results.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“The significance level defines how strong the sample evidence must be to conclude an effect exists in the population.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“Understanding this relationship is fairly straight forward. RSS represents the variability that your model explains. Higher is usually good. SSE represents the variability that your model does not explain. Smaller is usually good. TSS represents the variability inherent in your dependent variable. Or, Explained Variability + Unexplained Variability = Total Variability”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“SSE is a measure of variability. As the points spread out further from the fitted line, SSE increases. Because the calculations use squared differences, the variance is in squared units rather the original units of the data. While higher values indicate greater variability, there is no intuitive interpretation of specific values. However, for a given data set, smaller SSE values signal that the observations fall closer to the fitted values. OLS minimizes this value, which means you’re getting the best possible line.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“P-values indicate the strength of the sample evidence against the null hypothesis. If it is less than the significance level, your results are statistically significant.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“A beautiful aspect of regression analysis is that you hold the other independent variables constant by merely including them in your model!”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“It specifies how strongly the sample evidence must contradict the null hypothesis before you can reject the null for the entire population.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“OLS regression squares those residuals so they’re always positive. In this manner, the process can add them up without canceling each other out.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“correlation does not mean that the changes in one variable actually cause the changes in the other variable.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“The effect is the difference between the population value and the null hypothesis value. The effect is also known as population effect or the difference.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“You can think of the null as the default theory that requires sufficiently strong evidence in your sample to be able to reject it.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“When the p-value is low, the null must go. If the p-value is high, the null will fly.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“Pearson’s correlation measures only linear relationships. Consequently, if your data contain a curvilinear relationship, the correlation coefficient will not detect it.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“Correlations have a hypothesis test. As with any hypothesis test, this test takes sample data and evaluates two mutually exclusive statements about the population from which the sample was drawn. For Pearson correlations, the two hypotheses are the following: Null hypothesis: There is no linear relationship between the two variables. ρ = 0. Alternative hypothesis: There is a linear relationship between the two variables. ρ ≠ 0. A correlation of zero indicates that no linear relationship exists. If your p-value is less than your significance level, the sample contains sufficient evidence to reject the null hypothesis and conclude that the correlation does not equal zero. In other words, the sample data support the notion that the relationship exists in the population.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“What is a good correlation? How high should it be? These are commonly asked questions. I have seen several schemes that attempt to classify correlations as strong, medium, and weak. However, there is only one correct answer. The correlation coefficient should accurately reflect the strength of the relationship. Take a look at the correlation between the height and weight data, 0.705. It’s not a very strong relationship, but it accurately represents our data. An accurate representation is the best-case scenario for using a statistic to describe an entire dataset.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“Observed values of the dependent variable are the values of the dependent variable that you record during your study or experiment along with the values of the independent variables. These values are denoted using Y. Fitted values are the values that the model predicts for the dependent variable using the independent variables. If you input values for the independent variables into the regression equation, you obtain the fitted value. Predicted values and fitted values are synonyms.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“When the p-value is greater than the significance level, your sample data don’t provide enough evidence to conclude that the effect exists.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“Pearson’s correlation coefficient is unaffected by scaling issues. Consequently, a statistical assessment is better for determining the precise strength of the relationship.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“In statistics, correlation is a quantitative assessment that measures both the direction and the strength of this tendency to vary together.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“Confidence intervals incorporate the uncertainty and sample error to create a range of values the actual population value is likely to fall within.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions

“Continuous variables can take on almost any numeric value and can be meaningfully divided into smaller increments, including fractional and decimal values. You often measure a continuous variable on a scale. For example, when you measure height, weight, and temperature, you have continuous data. Categorical variables have values that you can put into a countable number of distinct groups based on a characteristic. Categorical variables are also called qualitative variables or attribute variables. For example, college major is a categorical variable that can have values such as psychology, political science, engineering, biology, etc.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“For a good model, the residuals should be relatively small and unbiased. In statistics, bias indicates that estimates are systematically too high or too low. Unbiased estimates are correct on average.”
― Jim Frost, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models

“In other words, it is the probability that you say there is an effect when there is no effect.”
― Jim Frost, Hypothesis Testing: An Intuitive Guide for Making Data Driven Decisions