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Stat 135 Midterm Review

# Stat 135 Midterm Review - Linear Regression Remember that...

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Linear Regression - Remember that correlation tells us the linear relationship between two variables but does not tell us about predicting one variable from another - In the given output, the explanatory variable will be under constant and the response will be the variable at the top of the output - Regression line y = ax + b, where a = variable coeff where b = constant coeff from output - To predict y value from x, we simply input the x value into the equation or vice versa - We will not get the same formula if we switch the variables - Only works if there is a somewhat strong linear relationship between variables - R-squared = % of variability in Y accounted for by X, Correlation = (sign of a) * sqrt (R²) - Extrapolation is bad!!!! We cannot predict values outside the range of our data!! Probability - Probability of an event will be between 0 or 1 and the sum of all probabilities is 1 - Remember that if two outcomes are disjoint, then the probability of both is the sum of their probabilities, meaning P(A or B) = P(A) + P(B). (picking out a red or blue shirt) - If events are independent, then the probability of both is the multiplication of each probability, meaning P(A and B) = P(A) * P(B). (think of rain today and rain tomorrow) - Law of averages tells us that probabilities stabilize in the long run - LOA does not mean that if we see a string of heads there is a better chance of seeing a tail - Each event is independent, so the next event will have the same prob. as it should Sampling Distributions (Use when looking at average of sample or proportions) - The sampling distribution will be normal no matter what the original distribution looks like and it will have mean = original mean, and sd_new = sd_old / sqrt(n) - Two concepts to remember about sampling distributions o String idea – meaning that as we take more and more samples the sampling distribution gets pulled upward at the true mean, and the sides shrink. The sides shrinking corresponding to the standard deviation getting smaller and smaller o In or out of box – meaning that when we are trying to figure out what is more likely with either a small or large sample, draw a line where the average or median is. Then draw a box around the probability you are trying to compare with. If the line is inside the box then you want the larger sample, outside the box you want the smaller sample - When we look at proportions, the sampling distribution has mean p, which is the true proportion and sd = sqrt(p(1-p) / n).

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Stat 135 Midterm Review - Linear Regression Remember that...

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