Grad Rate 2016 GPA_Avg SAT_Med Perc_Freshmen_Pell Ratio 0.917 0.872 0.724 0.706 0.675 0.865 0.764 0.743 0.501 0.939 0.832 0.82 0.789 0.645 0.598 0.581 0.316 0.701 0.582 0.509 0.466 0.434 0.362 0.6 0.548 0.528 0.456 0.303 0.413 0.374 3.87 3.94 3.79 3.62 3.62 3.6 3.64 3.5 3.18 3.95 3.75 3.97 3.69 3.61 3.32 3.49 2.93 3.49 3.5 3.08 3.37 3.32 3.2 3.5 3.2 3.36 3.26 3.12 3.4 3.29 1397 1175 1271 1081 1204 1303 1199 1142 902 1479 1222 1211 1217 1086 960 1080 962 1072 1067 990 1088 1069 993 1110 951 1131 990 961 1029 992 0.23 0.409 0.333 0.256 0.199 0.133 0.188 0.193 0.632 0.135 0.185 0.074 0.145 0.283 0.441 0.433 0.679 0.234 0.281 0.494 0.319 0.36 0.479 0.512 0.366 0.224 0.536 0.488 0.385 0.515 9 11 9 19 12 5 13 13 32 2 11 14 14 34 20 18 65 19 8 19 17 13 15 19 19 18 28 16 23 13 normal score -2.141198121 -1.660697611 -1.400745061 -1.211232131 -1.057414228 -0.92524456 -0.807541042 -0.700090213 -0.600178776 -0.505933654 -0.41598722 -0.329291347 -0.245006223 -0.162429373 -0.08094729 0 0.08094729 0.162429373 0.245006223 0.329291347 0.41598722 0.505933654 0.600178776 0.700090213 0.807541042 0.92524456 1.057414228 1.211232131 1.400745061 1.660697611 Step 3: Find the indicated values and report them below. Regression sum of squares (SSRegr), rounded to four decimal places is 0.8147. degrees of freedom for SSRegr: k = 3 3 Residual sum of squares (SSResid), rounded to four decimal places is 0.1686. degrees of freedom for SSResid: n − (k+ 1) = 26 Compute the F test statistic using the rounded values reported above. (Round the statistic to two decimal places. Note that your number below will not match the F statistic from the output exactly due to using the rounded values above.) SSRegr "numerator SSResid F = df denominator df denominator This test statistic has an F probability distribution with df, df Thus, there appears one of the three predictors. 0.0003 82.9 42.88 26 Step 4: The test statistic found in step 3 has a P-value < 0.00001 smallest number the P-value is less than). Se= Vs 26 e 41.89 numerator Provide the linear multiple regression model with all values. (Round the intercept as well as the GPA and Pell Gran coefficients to three decimal places. Round the SAT coefficient to four decimal places.) 2016 6-year graduation rate = -1.071 -1.071 +0.403 0.403 GPA + 0.0003 SAT - 0.163 SSResid n (k+ 1) 26 0.081 0.112 appears to be a useful linear relationship between y and at least 5: What is the value of R2 from the analysis. (Round your answer to one decimal place.) 82.9 % and 0.163 % Pell Grant What is the estimated random error standard deviation? (Round your answer to three decimal places.) 0.00001. (Pick the 0.081 Recall that just because the model utility test performed in steps 2-4 indicates that the multiple regression model is useful, it does not automatically follow that all the predictors included in the model contribute to the usefulness of the model. It is desirable that a useful model has both a large R² value and a small se value but also has relatively few predictor variables whose roles are easily interpreted. Step 6: Create a simple linear regression model that predicts the 2016 6-year graduation rate with average high school GPA among college freshmen. The model under consideration is y = x + ₁x₁ + e where y is the 2016 6-year graduation rate, x₁ is the average high school GPA among college freshmen, and e is the random deviation associated with each value of y. The random deviations are assumed to be normally distributed with a mean value of 0 and constant variance of ². Create a simple linear regression model to predict the 2016 6-year graduation rate using only the average high school GPA among college freshmen. Let the significance level be a = 0.05. Save the standardized residuals from the analysis so that the assumption on the random deviation, e, can be verified with a normal probability plot. To create a normal probability plot, also known as a Q-Q plot, of the standardized residuals, you will need the normal_scores.csv file that contains normal scores for a n = 30 sample. Save the Standardized Residuals from the analysis, sort them in ascending order from the output and pair them with the normal scores from the document to form (normal percentile, Standardized Residuals) ordered pairs for the normal probability plot.