SAT Scores by State A common objective for many school administrators is to incr
ID: 3070976 • Letter: S
Question
SAT Scores by State A common objective for many school administrators is to increase the number of students taking SAT and ACT tests from their school. The data from each state from 2003 are reflected in the scatterplot. 1) 1220 1 1140 E 1100 1060 1020 980 a) What is the explanatory variable? 0 |0 20 30 40 50 60 70 80 90 b) Estimate the correlation. SA TParticipation In an effort to decide if there is an association between the year of a postal increase and the new postal rate for first class mail, the data were gathered from the United States Postal Service. In 1981, the United States Postal Service changed their rates on March 22 and November 1. This information is shown in the table below. US Postal Rate vs Year Rate-19.93+0.01015 Year ear 1971 0.08 1974 0.10 1975 0.13 1981 | 0.18 1981 0.20 1985 0.22 3.20 1991 0.29 a) Do you think a linear model is appropriate here? Explain.Explanation / Answer
Question 1 :
The scatter plot represents the average score in SAT examination versus the total number of students appearing for the SAT exam.
a. The explanatory variable is the number of students appearing in the SAT examination.
The scatter plot indicates the year of increase versus the new postal rates for first class mail service.
a.) The scatter plot is indicative of the fact that with time the postal rates seemed to increase at a constant rate on an average and thus represents a linear trend.Hence a linear model is definitely appropriate.
b.) By studying the coeffecients of the fitted linear regression model, we observe that the slope of the line is 0.010152. This can be interpreted as, for increase in time period by one year, the new postal rates is expected to increase by 0.010152 above the present.
c.) The intercept is -19.928. Mathematically it can be interpreted as when the time period is zero , that is at origin of time the postal rate is expected to be -19.928.
e.) R2 is explained as the proportion of explained variablity in y to the total variability of y. In simple terms, it explains how much well the regression model is able to capture the information in the data. So higher the value, the better.In this problem, the linear regression model is able to explain 98.82% of the change in postal rates with time as the explanatory variable.
f.) Maybe overestimating the postal rates will be a more serious issue. So a lesser predicted value than the actual postal rates for any consumer would be better.
g.) According to the model, the predicted postal rates for 2018 is approximately 0.558. The reservation to be made during such predictions is that the situations whrn there is a sudden surge or dip in postal rates is definitely ignored and also it is assumed that the postal rates will hopefully keep increasing with time at a more or less constant rate.
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