HW 01 model solution-1

# HW 01 model solution-1 - HW 1 Model Solution 1.8 Breakfast...

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HW 1 Model Solution 1.8 Breakfast cereal. The number of calories and number of grams of sugar per serving were measured for 36 breakfast cereals. The data are in the file cereal.sas7bdat. We are interested in trying to predict the number of calories using the sugar content. a. Make a scatterplot and comment on what you see. The scatterplot (shown below) shows a moderate positive linear relationship between Calories and Sugar. Scatter Plot

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b. Find the least squares regression line for predicting calories based on sugar content. Based on the regression output given below, the least squares regression line is ° 87.42769 2.48081* Calories Sugar = + Linear Regression Results The REG Procedure Model: Linear_Regression_Model Dependent Variable: Calories Number of Observations Read36 Number of Observations Used36 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 1 4567.22217 4567.22217 12.30 0.0013 Error 34 12626 371.35846 Corrected Total 35 17193 Root MSE 19.27066 R-Square 0.2656 Dependent Mean 101.60278 Adj R-Sq 0.2440 Coeff Var 18.96667 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Intercept 1 87.42769 5.16268 16.93 <.0001 Sugar 1 2.48081 0.70740 3.51 0.0013 c. Interpret the value (not just the sign) of the slope of the fitted model in the context of this setting. For every additional gram of sugar in a serving of cereal, the expected calories increase by about 2.48 calories.
1.9 More breakfast cereal. a. How many calories would the fitted model predict for a cereal that has 10 grams of sugar? Using the regression equation we have ° 87.42769 2.48081* (10) 112.2358 Calories = + = . The predicted value given in SAS EG is ° 112.23581623 Calories = . b. Cheerios has 110 calories but just 1 gram of sugar. Find the residual for this data point. The residual value given in SAS EG is 20.091497175. c. Does the linear regression model appear to be a good summary of the relationship between calories and sugar content of breakfast cereals? The scatterplot with the fitted line shown below shows quite a bit of scatter around the fitted line. The value 2 0.2656 R = indicates that only 26.56 of the variability in Calories is explained by the linear relationship between Calories and Sugar. Generated by the SAS System ('Local', XP_PRO) on October 07, 2013 at 10:20:19 PM

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1.17 Enrollment in mathematics courses. Total enrollments in mathematics courses at a small liberal arts college were obtained for each semester from Fall 2001 to Spring 2012. The academic year at this school consists of two semesters, with enrollment counts for Fall and Spring each year as given in the data set mathenrollment.sas7bdat. The variable AYear indicates the year at the beginning of the academic year.
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