Regression Analysis Quiz
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Questions and Answers

What is one major use of regression analysis?

  • To eliminate outliers from data
  • To determine the strength of predictors (correct)
  • To develop complex algorithms
  • To create random data sets

    • How does regression analysis help in forecasting effects?

  • It indicates how much the dependent variable changes with changes in independent variables. (correct)
  • It calculates exact future values.
  • It provides estimated means of the data.
  • It replicates existing data trends without analysis.

    • Which equation represents the least square regression line?

  • y = ax + b (correct)
  • y = 1/x + b
  • y = bx + a
  • y = mx + c

    • What does the method of least squares accomplish in regression analysis?

    <p>Minimizes the sum of the squares of vertical deviations.</p> Signup and view all the answers

    In a linear regression, what is the significance of points indicating a 'linear relationship' on the plot?

    <p>They allow for the use of the method of least squares to find the regression line.</p> Signup and view all the answers

    What percent of physical therapists earned less than Php 105,900?

    <p>90%</p> Signup and view all the answers

    How many percent of physical therapists earned more than Php 74,480?

    <p>50%</p> Signup and view all the answers

    What is the calculation to find the percentile of Benedict’s score of 602?

    <p>576/900 * 100</p> Signup and view all the answers

    What is the value of the first quartile (Q1) if there are 25% of observations below it?

    <p>25%</p> Signup and view all the answers

    If 40% of physical therapists earned between Php 74,480 and Php 105,900, what percent earned less than Php 74,480?

    <p>50%</p> Signup and view all the answers

    How many data values fall below the 50th percentile in a given dataset?

    <p>50%</p> Signup and view all the answers

    What defines the third quartile (Q3) in a dataset?

    <p>75% of observations below Q3</p> Signup and view all the answers

    What is the process to find the first quartile (Q1) of a dataset?

    <p>Find the median of data values below the median.</p> Signup and view all the answers

    What does the variable $X$ represent in the mean calculation?

    <p>Mean score</p> Signup and view all the answers

    How is the class mark ($X_m$) calculated?

    <p>By summing lower and upper interval and dividing by 2</p> Signup and view all the answers

    What is the sum of frequencies ($ extstyle abla f$) in the given example?

    <p>50</p> Signup and view all the answers

    Which value represents the total for $ extstyle abla fX_m$ in the solution?

    <p>4110</p> Signup and view all the answers

    What is the formula used to calculate the mean from grouped data?

    <p>$X = \frac{\sum fX_m}{N}$</p> Signup and view all the answers

    How many students scored between 80 and 84 based on the provided frequency distribution?

    <p>14</p> Signup and view all the answers

    What does a correlation coefficient r < 0 indicate about the relationship between x and y?

    <p>y decreases as x increases</p> Signup and view all the answers

    What would happen if we incorrectly counted the frequency for the class interval 90-94 as 10 instead of 9?

    <p>The calculated mean would increase.</p> Signup and view all the answers

    Which of the following calculations is necessary to find $ extstyle abla fX_m$?

    <p>Multiplying frequency by the respective class mark</p> Signup and view all the answers

    What does it mean if the absolute value of the correlation coefficient |r| is near 1?

    <p>the linear relationship is strong</p> Signup and view all the answers

    Given the data X = 4, 8, 12, 16 and Y = 5, 10, 15, 20, what is the sign of the correlation coefficient r?

    <p>positive</p> Signup and view all the answers

    What does a correlation coefficient r = 1 signify about the relationship between two variables?

    <p>perfect positive correlation</p> Signup and view all the answers

    If |r| is near 0, what can be inferred about the linear relationship between x and y?

    <p>it is weak or non-existent</p> Signup and view all the answers

    What are the necessary calculations to determine the correlation coefficient from given data?

    <p>calculating Σx, Σy, Σx^2, Σy^2, and Σxy</p> Signup and view all the answers

    What is indicated if the correlation coefficient r is close to -1?

    <p>there is a strong negative linear relationship</p> Signup and view all the answers

    Which expression correctly represents the calculation of the correlation coefficient based on Σx, Σy, Σxy, Σx^2, and Σy^2?

    <p>r = \frac{nΣxy - ΣxΣy}{\sqrt{(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)}}</p> Signup and view all the answers

    What does the variable 'm' represent in the equation of a line?

    <p>The slope or gradient of the line</p> Signup and view all the answers

    Which step involves calculating the total of x squared and the product of x and y?

    <p>Step 1</p> Signup and view all the answers

    What is the formula used to calculate the intercept 'b'?

    <p>b = Σy - m ΣxN</p> Signup and view all the answers

    If the number of data points N is 5, what is the total value of Σx for the provided data?

    <p>26</p> Signup and view all the answers

    In the example data, what is the value of Σy?

    <p>41</p> Signup and view all the answers

    Which calculation is NOT part of deriving the slope 'm'?

    <p>Calculating Σx squared</p> Signup and view all the answers

    What represents the value where the line crosses the Y-axis?

    <p>Y-intercept (b)</p> Signup and view all the answers

    What is the product of the last row of x and y values for calculating Σxy in the example?

    <p>135</p> Signup and view all the answers

    If you sum all x^2 values (x squared), what operation helps obtain Σx^2?

    <p>Adding each squared value together</p> Signup and view all the answers

    What might be a misconception about the steps to find the line of best fit?

    <p>The intercept does not involve Σy</p> Signup and view all the answers

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