Question: 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.

Perform a linear regression with the Response (dependent variable) math score and the variable IQ as the Predictor (independent variable) . Store/save the Residuals and Fitted values. These will be stored in the fourth and fifth columns of the data worksheet. The output (shown here in Minitab) 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

Residual Error 18 285.90 15.88

Total 19 520.20

1. Explain this equation. Discuss slope as change in Y per unit change in X in context of the variables used in this problem
2. Create a scatter plot of the measurements by selecting IQ as the predictor (x-variable) and math score as the response (y-variable). Describe the relationship between math score and IQ .
3. 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 Plo (or Q-Q plot)t. To get a residual plot, simply create a Scatterplot using the Residuals as the y-variable and the Fitted Values as the x-variable. Now create a probability plot (Q-Q plot if using SPSS) of the residuals. In Minitab, we are provided the results of a test of the null hypothesis that the data follows a normal distribution. Based on these two graphs and what you have learned about hypothesis testing, what interpretations do you come to regarding the assumptions of constant variance and normality?
4. The least squares regression line for predicting math score from IQ is given in the above output. What is the fitted regression line (i.e. regression equation)?
5. What do the values in the FITS and RES columns represent?
6. Based on the output, what is the test of the slope for this regression equation? That is, provide the null and alternative hypotheses, the test statistic, p-value of the test, and state your decision and conclusion.

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