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- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/08%3A_Multiple_Linear_Regression/8.01%3A_Multiple_RegressionsIt frequently happens that a dependent variable (y) in which we are interested is related to more than one independent variable. If this relationship can be estimated, it may enable us to make more pr...It frequently happens that a dependent variable (y) in which we are interested is related to more than one independent variable. If this relationship can be estimated, it may enable us to make more precise predictions of the dependent variable than would be possible by a simple linear regression. Regressions based on more than one independent variable are called multiple regressions.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/02%3A_Sampling_Distributions_and_Confidence_Intervals
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/zz%3A_Back_Matter/10%3A_Index
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/11%3A_Biometric_Labs/11.05%3A_Biometrics_Lab_5Before you create this regression model, you must examine the relationships between each of the five predictor variables and biomass (the response variable). The response variable (y-variable) is Bio ...Before you create this regression model, you must examine the relationships between each of the five predictor variables and biomass (the response variable). The response variable (y-variable) is Bio and the five predictor variables are the x-variables. You will compare the adjusted R2, regression standard error, p-values for each coefficient, and the residuals for each model. Now remove the LEAST significant variable (highest p-value) and repeat the steps using only the remaining variables.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/07%3A_Correlation_and_Simple_Linear_Regression/7.03%3A_Population_ModelWe use the means and standard deviations of our sample data to compute the slope (b1) and y-intercept (b0) in order to create an ordinary least-squares regression line. But we want to describe the rel...We use the means and standard deviations of our sample data to compute the slope (b1) and y-intercept (b0) in order to create an ordinary least-squares regression line. But we want to describe the relationship between y and x in the population, not just within our sample data. We want to construct a population model. Now we will think of the least-squares line computed from a sample as an estimate of the true regression line for the population.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/01%3A_Descriptive_Statistics_and_the_Normal_Distribution/1.02%3A_Probability_DistributionComputing probabilities for continuous random variables are complicated by the fact that there are an infinite number of possible values that our random variable can take on, so the probability of obs...Computing probabilities for continuous random variables are complicated by the fact that there are an infinite number of possible values that our random variable can take on, so the probability of observing a particular value for a random variable is zero. To find the probabilities associated with a continuous random variable, we use a probability density function (PDF).
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/07%3A_Correlation_and_Simple_Linear_Regression/7.02%3A_Simple_Linear_RegressionOnce we have identified two variables that are correlated, we would like to model this relationship. We want to use one variable as a predictor or explanatory variable to explain the other variable, t...Once we have identified two variables that are correlated, we would like to model this relationship. We want to use one variable as a predictor or explanatory variable to explain the other variable, the response or dependent variable. In order to do this, we need a good relationship between our two variables. The model can then be used to predict changes in our response variable. A strong relationship between the predictor variable and the response variable leads to a good model.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/05%3A_One-Way_Analysis_of_Variance
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/05%3A_One-Way_Analysis_of_Variance/5.01%3A_Analysis_of_VarianceWe can use the ratio of \(S_B^2/ S_W^2\) as a test statistic to test the null hypothesis that \(H_0: \mu_1= \mu_2= \mu_3= …= \mu_k\), which follows an F-distribution with degrees of freedom \(df_1= k ...We can use the ratio of \(S_B^2/ S_W^2\) as a test statistic to test the null hypothesis that \(H_0: \mu_1= \mu_2= \mu_3= …= \mu_k\), which follows an F-distribution with degrees of freedom \(df_1= k – 1\) and \(df_2= N –k\) (where k is the number of populations and N is the total number of observations (\(N = n_1 + n_2+…+ n_k\)).
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/04%3A_Inferences_about_the_Differences_of_Two_Populations/4.01%3A_Inferences_about_Two_Means_with_Independent_Samples_(Assuming_Unequal_Variances)If the confidence interval contains all positive values, we find a significant difference between the groups, AND we can conclude that the mean of the first group is significantly greater than the mea...If the confidence interval contains all positive values, we find a significant difference between the groups, AND we can conclude that the mean of the first group is significantly greater than the mean of the second group. We have all negative values, so we can conclude that there is a significant difference in the mean number of cavity trees AND that the mean number of cavity trees in the Adirondack forests is significantly less than the mean number of cavity trees in the Monongahela Forest.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/08%3A_Multiple_Linear_Regression/8.02%3A_Software_SolutionThe best representation of the response variable, in terms of minimal residual sums of squares, is the full model, which includes all predictor variables available from the data set. A researcher want...The best representation of the response variable, in terms of minimal residual sums of squares, is the full model, which includes all predictor variables available from the data set. A researcher wants to be able to define events within the x-space of data that were collected for this model, and it is assumed that the system will continue to function as it did when the data were collected.
