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Saturday, April 10

  1. page 9. Linear, quadratic and exponential regression edited ... y = ax2 + bx + c for a quadratic regression y = abx + c for an exponential regression Usual…
    ...
    y = ax2 + bx + c for a quadratic regression
    y = abx + c for an exponential regression
    Usually, the regression line will be created using a set of data. Subsequently, the equation of the line found through the regression process will be used to make a prediction of an output (y) value for a proposed value of the input (x).
    R (Correlation Coefficient )
    Measures the strength of the linear relationship. It doesn’t show a curved relationship even if it’s a strong one. As R is closer to 0 a straight line is a poorer description of the data [bad fit], but when its close to either -1 or 1, it’s a strong fit. Below are some examples of correlation coefficients. The one all the way in the lower right corner when r = -.99 has the best fit of all 6 graphs. With such a high r, it shows how well the points actually fit to the line. The one in the upper left corner on the other hand has the worst fit since r = 0, it demonstrates no fit.
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  2. page 9. Linear, quadratic and exponential regression edited Regression ... the relationship. The line is given in the form of an equation: y = mx + b fo…

    Regression
    ...
    the relationship. The line is given in the form of an equation:
    y = mx + b for a straight line regression
    y = ax2 + bx + c for a quadratic regression
    y = abx + c for an exponential regression

    R (Correlation Coefficient )
    ...
    to 0 ita straight line is a less fit [bad],poorer description of the data [bad fit], but when
    {Picture_2.png}
    R^2 is known as the coefficient of determination which is the proportion of the y values explained by the least squares regression line. A high R^2 is a good linear fit.
    ...
    Answers:
    Example 1
    1. LSRL =LSRL: y =
    ...
    - 5.317 (equation that best matches the data) R = .921 (correlation coeff), R^2 =
    2. y = (1.244)(50) - 5.317 = 56.883 years old
    Residual = O - P
    ...
    Residual = -5.883
    Example 2
    1. LSRL =LSRL: y = (114.055)(.944)^X(114.055)(.944)X
    2. ln(y) = -0.0576X + 4.737
    3. ln(y) = (-0.0576)(45) + 4.737
    ...
    (B) 49% of the variability in home heating bills can be explained by home size.
    (C) For each added square foot of home size, heating bills increased by 70 cents.
    ...
    49 cents.
    Answer: b- r = .7 therefore r^2 = .49 r^2 explains the proportion of values the least squares regression line represents.
    http://www.devexpress.com/Help/?document=XtraCharts/CustomDocument6231.htm&levelup=true
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  3. page 7. Histograms edited What is a Histogram? ... bars). The area height of each ... to the variable being studied w…
    What is a Histogram?
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    bars). The areaheight of each
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    to the variable being studied whilenumber of times a particular set of values has occurred its width
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    the x-axis interval.interval (the span of that particular set of numbers).
    Histogram Example:
    A histogram is made by graphing a set of values, for example, like the number set {1,2,2,3,3,3,3,4,4,5,6}. This would be the graph:
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  4. page 6. 5-number summary and box plots edited ... Hence the right answer is Plot 1. ¹ Question 2: Consider the boxplot below {box_plot_madnes…
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    Hence the right answer is Plot 1. ¹
    Question 2: Consider the boxplot below
    {box_plot_madnessss.png}
    Which of the following statements are true?
    I. The distribution is skewed right.
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  5. page 6. 5-number summary and box plots edited ... 10. Median of the scores obtained by Ethan = Middle quartile = 78 Hence the right answer is P…
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    10. Median of the scores obtained by Ethan = Middle quartile = 78
    Hence the right answer is Plot 1. ¹
    ...
    the boxplot below.
    {file:///Users/papazian/Desktop/Picture%201.png}
    {file:///Users/papazian/Desktop/Picture%201.png}
    {file:///Users/papazian/Desktop/Picture%201.png}
    below
    Which of the following statements are true?
    I. The distribution is skewed right.
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  6. page 6. 5-number summary and box plots edited ... Question 2: Consider the boxplot below. {file:///Users/papazian/Desktop/Picture%201.png} {…
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    Question 2: Consider the boxplot below.
    {file:///Users/papazian/Desktop/Picture%201.png}
    {Picture_1.png} {file:///Users/papazian/Desktop/Picture%201.png}{file:///Users/papazian/Desktop/Picture%201.png}
    {file:///Users/papazian/Desktop/Picture%201.png}
    Which of the following statements are true?
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  7. page 6. 5-number summary and box plots edited ... 3. Draw a box with ends through the points for the first and third quartiles. Then draw a vert…
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    3. Draw a box with ends through the points for the first and third quartiles. Then draw a vertical line through the box at the median point. Then, draw the whiskers (or lines) from each end of the box to the smallest and largest values. 2 {http://kwiznet.com/px/homes/i/math/G10/Statistics/statistics_box_and_wisker_plots1.gif}
    SAT/AP Style Questions
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    is the equivalentbox-and-whiskerequivalent box-and-whisker plot of
    Year
    Percentage of scores
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  8. page 5. Normal Distribution edited Normal Distribution: A function that represents the distribution of many random variables. This is…
    Normal Distribution: A function that represents the distribution of many random variables. This is represented by a Normal Model, usually as a bell-shaped curve.
    {NormalCurve.png}
    ...
    proving its normalitynormality. Thus, you can always assume that 50% of the data are greater than the mean and 50% are less than the mean.
    - The graph is an idealized representation of the data's histogram
    - Every normal set of data has a mean and a standard deviation
    o They are used as the parameters of the set of data
    - The figure above shows the relationship between standard deviation and the proportion of data in various parts of the bell curve. As you can see, roughly 68% of the data occur between 1 standard deviation less than the mean and 1 standard deviation greater than the mean. 95% are within 2 standard deviations of the mean, and 99.7% are within 3 standard deviations of the mean.
    - Z-score: tells you how many standard deviations a value is from the mean. Equation: {Picture_3.png}
    The set of data must have only one peak and be symmetric to start, it cant just become normal.
    ...
    Normalcdf(93,1E99,87,2.7) = 1.31%..GOOD JOB RACHEL!!
    If Dylan scored in the top 25% of the class, then what was the lowest possible grade she could have gotten?
    Invnorm(.75,87,2.7)= 88.82
    You could also answer less quantitative questions.
    Example:
    Math SAT scores for students in a particular state are normally distributed with a mean of 610 and a standard deviation of 50 points. Are the following statements true or false?
    1. If you choose a student at random, their most likely score is 610 (TRUE)
    2. A student should be considered above average if they score a 600 (FALSE, more than half of the data are higher than 600, since exactly half of the data are above 610.)
    3. More than half the students in the state scored between 560 and 660 (TRUE, this is the span from 1 standard deviation below the mean to 1 standard deviation above the mean, which includes roughly 68% of the data).
    4. It should be considered pretty special to score above 760. (TRUE, since 0.3% of the data are more than 3 standard deviations from the mean, this means half of that, or 0.15%, is above 760 and 0.15% is below 460. Being in the top 0.15% is pretty special indeed!)
    5. If you choose a student at random, they are just as likely to have scored a 600 as a 700. (FALSE, because the distribution is symmetric, points with equal probability are equidistant from the mean. 620 is as likely as 600, and 520 is as likely as 700.)

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  9. page 4. Probability Distributions edited ... If you look at the graph of a probability distribution, the x values that correspond to high y…
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    If you look at the graph of a probability distribution, the x values that correspond to high y values have a higher probability of occurring. In other words, where the graph is high, the probability is also high and those x values are more likely to occur.
    Types Of Distributions
    ----------------------------------------------------------------------------------------------------------------------------------------- Normal
    Normal
    Distribution (Gaussian)
    Is a frequency distribution for a set of data, that usually results in a bell curve.
    The Bell Curve of the graph usually results in a single peak at the mode of the data.
    ...
    Also see Normal Normal Distribution Tab to understand
    Normal cdf is used to calculate probability of a normal curve. Learn how to compute by clicking the Normal Distribution Tab
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    a Normal DistributionDistribution. Note that the functions shown in the answers refer to functions available on the TI-84/84 graphing calculators
    The cost of treatment per patient for a certain medical problem was modeled by
    one insurance company as a normal distribution with mean $775 and standard
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