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Inferences for Slope definitions

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  • Regression Line
    A straight path that best fits the data points, showing the relationship between two quantitative variables.
  • Slope
    A value indicating the rate of change in the response variable for each unit increase in the explanatory variable.
  • Population Regression Line
    The true underlying linear relationship between variables for an entire group, not just a sample.
  • Linear Correlation
    A consistent, straight-line association between two variables, where changes in one predict changes in the other.
  • Null Hypothesis
    A starting assumption that there is no linear relationship between the variables, often represented as zero slope.
  • Alternative Hypothesis
    A claim that challenges the null, suggesting a nonzero slope and thus a linear relationship exists.
  • Alpha Level
    A threshold probability, such as 0.05, used to decide whether evidence against the null hypothesis is strong enough.
  • P-value
    A calculated probability that measures how likely the observed data would occur if the null hypothesis were true.
  • Confidence Interval
    A range of values, derived from data, that likely contains the true slope with a specified level of certainty.
  • Significance
    A determination that results are unlikely to have occurred by chance, often when the p-value is below the alpha level.
  • TI-84
    A graphing calculator commonly used to perform statistical tests and compute regression analysis efficiently.
  • LinRegTTest
    A calculator function that tests hypotheses about the slope of a regression line using sample data.
  • LinRegTInt
    A calculator function that constructs a confidence interval for the slope of a regression line.
  • Confidence Level
    The probability, such as 95%, that the calculated confidence interval actually contains the true slope.
  • Test Statistic
    A value computed from sample data that is used to decide whether to reject the null hypothesis.