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Lecture 4

SOC222 - Jan 31st Week 4.docx

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Department
Sociology
Course Code
SOC222H5
Professor
John Kervin

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1 SOC 222 -- MEASURING the SOCIAL WORLD Session #4 -- RAT  RAT RELATIONSHIPS Readings: Linneman: ch. 7 Kranzler: ch. 8: 79-87 Ch. 9: 90-93 Today’s Objectives: Know… 1. How to obtain and interpret a scatterplot with a fit line. 2. Similarity of a scatterplot and a crosstab 3. How a regression fit line indicates relationship direction and effect size 4. The parts of a linear equation 5. And understand covariance 2 6. How to get regression coefficients and R in SPSS 7. How to use a regression equation to make predictions 8. PVE measures of effect size for regressions, correlations, and comparing means 9. Correlation Terms to Know Scatterplot X and Y-axes Regression fit line Linear (equation) Coefficient Slope “b” Constant “a” Covariance Coefficient of determination R2 Proportion of variation explained (PVE) Correlation coefficient “r” Scatter RAT  RAT RELATIONSHIPS SCATTERPLOTS 2 Tells us: 1. Is there a relationship between the independent and dependent variable? 2. What direction would that relationship be? Is the relationship negative or positive? 3. How strong the relationship is. How much of an impact does the independent variable have on the dependent? RQ: Do immigrants settle in provinces, which are more urban? • Percent of provincial population living in cities • Percent of provincial population who are immigrants - Substantial effect size (big difference in the minimum and maximum) 3 - There is a positive relationship, as the percent immigrants increases so does the percent in cities Scatterplots & Crosstabs Percent in Cities Percent Immigrants: Low High High 0 3 Low 2 8 REGRESSION FIT LINE (The line of best fit) Gives us two things: 1. The effect size – how steep the slope is, the steeper the slope, the greater the effect. The steeper the slope the more the dependent variable is increasing with every 1 percent added to the independent variable 4 2. We get to see the direction of the relationship, upward sloping line. A downward sloping line tells us that the relationship is negative We can see: 1. 2. 3. LINEAR EQUATIONS - Any straight line on the graph can be presented by the equation - The y is the dependent variable and the x is the independent variable Y = a + b (X) Four parts: X, Y, a, b Variables Coefficients – b – is the slope of the line, b tells us how steep the line is. Every time x goes up by 1, b is the change in y. Also the measure of the effect size Constant – where the line crosses the y-axis 5 Slope • Every time the value of X increases by 1, this is how much the value of Y goes up – the variable b Finding the Regression Line Coefficients Covariance Variance is the “variation” or “dispersion” or “spread” of one variable 2 Variance = s = ∑ (x−́x) n−1 (x−x) (x−́x)(y−y) Step 1: (x−x) Step 2: (y−y) Step 3: (x−́x)(y−y) Step 4: ∑ (x−́x)(y−y) Step 5: ∑ (x−́x)(y−y) Covariance = N−1 NOTE: • ∑ • N - 1 The Logic of Covariance 1. One variable • Values: 1, 3, 5, 7, 9, 11 6 2. Product of Two Differences • Small: 2, 3 • Big: 11, 12 • A small difference times a small difference is a small number • 2 * 3 = 6 • A small difference times a big difference is a big number • 2 * 11 = 22 • A big difference times a big difference is a very big number • 11 * 12 = 132 • If a case is close to the mean on both X and Y, • If a case is far from the mean on both X and Y, EG #1: X Y Differences from mean for X, Y 1 2 -2, -2 3 4 0, 0 5 6 2, 2 • Product results: 4, 0, 4 • Sum: 8 EG #2: X Y Differences from mean for X, Y 1 2 -2, -2 3 6 0, -2 5 4
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