28 - 28Simple Linear Regression - Solutions 1 Relationship...

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Unformatted text preview: 28Simple Linear Regression - Solutions 1 Relationship Between Eighth Grade IQ and Ninth grade Math Score For a statistics class project, students examined the relationship between x = 8 th grade IQ and y = 9 th grade math scores for 20 students. The data are displayed below. Student Math Score IQ Abstract Reas 1 33 95 28 2 31 100 24 3 35 100 29 4 38 102 30 5 41 103 33 6 37 105 32 7 37 106 34 8 39 106 36 9 43 106 38 10 40 109 39 11 41 110 40 12 44 110 43 13 40 111 41 14 45 112 42 15 48 112 46 16 45 114 44 17 31 114 41 18 47 115 47 19 43 117 42 20 48 118 49 Use Minitab on the dataset Finals found in the Datasets folder in ANGEL. Do Stat>Regression>Regression and enter in the Response window the variable math score and in the Predictors window enter IQ. Click Storage and then Residuals and Fits. These will be stored in columns C3 and C4 and named as RESI1 and FITS1. Your output should look as follows: Regression Analysis: Math Score versus IQ The regression equation is Math Score = - 21.0 + 0.567 IQ Predictor Coef SE Coef T P Constant -21.04 16.00 -1.32 0.205 IQ 0.5666 0.1475 3.84 0.001 S = 3.98537 R-Sq = 45.0% R-Sq(adj) = 42.0% Analysis of Variance Source DF SS MS F P Regression 1 234.30 234.30 14.75 0.001 1 Residual Error 18 285.90 15.88 Total 19 520.20 a. Explain this equation. Discuss slope as change in Y per unit change in X in context of the variables used in this problem The slope indicates for a unit change in X, Y will change by the amount and direction of the slope. So here, for a 1 unit increase in IQ the predicted math score will increase by 0.567 points. b. Create a scatter plot of the measurements by Graph > Scatter Plot > Simple , and select IQ as the predictor (x-variable) and math score as the response (y-variable). Describe the relationship between math score and IQ . 120 115 110 105 100 95 50 45 40 35 30 IQ Math Score Scatterplot of Math Score vs I Q There is a positive relationship between math score (the response variable) and IQ (the explanatory variable) c. One of the students with a high IQ (number 17) appears to be an outlier. With a sample size of only 20 this can affect our normality assumption. Also, the constant variance assumption could be compromised. We can visual check for constant variance using a Residual Plot and test for normality using a Probability Plot. To get a residual plot go to Graph > Scatterplot > Simple and enter RESI1 as y- variable and FITS1 as x-variable. Click OK. For the probability plot check of normality, go to Graph > Scatterplot > Single and enter RESI1 in the graph variables window. This provides a test of the null hypothesis that the data follows a normal distribution. hypothesis that the data follows a normal distribution....
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This note was uploaded on 08/01/2011 for the course STAT 101 taught by Professor Thomas during the Spring '11 term at Penn State.

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28 - 28Simple Linear Regression - Solutions 1 Relationship...

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