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. (B)</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. (B)</p> Signup and view all the answers

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

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

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

<p>50% (B)</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 (D)</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% (D)</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% (C)</p> Signup and view all the answers

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

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

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

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

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

<p>Mean score (B)</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 (C)</p> Signup and view all the answers

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

<p>50 (A)</p> Signup and view all the answers

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

<p>4110 (D)</p> Signup and view all the answers

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

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

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

<p>14 (B)</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 (D)</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. (C)</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 (A)</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 (A)</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 (D)</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 (D)</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 (C)</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 (A)</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 (D)</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)}} (A)</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 (A)</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 (D)</p> Signup and view all the answers

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

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

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

<p>41 (B)</p> Signup and view all the answers

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

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

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

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

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