Question

Just need help with part (b)

Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Suppose these are the last few national mean scores, on a scale of 0 to 500. Year 1990 1992 1996 2000 2003 2005 2008 2011 2013 Score 263 266 271 272 278 279 281 283 285 (a) Make a time plot of the mean scores, by hand. This is just a scatterplot of score against year. There is a slow linear increasing trend Score 300「 Score 300 290 290 280 280 270 270 260 260 250 Year 250 O 1990 1990 2000 2010 20 2010 Ye 2000 2020

Answer 1

Interpretation:

The scatter plot enables that the two quantitative variables Year (X) and Score (Y) are positively linearly correlated.

The direction of the two variables is the same and the plot showing the upward linear trend. The trend is slow linear increasing trend.

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The computati on table 199026.3 1992266 1996 271 2000 272 2003 278 2005 279 2008 281 2011 283 2013 285 (x-X)(r-?) 147.9996 93.333 25.9998 6.6666 2.6667 11.0001 34.0002 69.0003 106.3337 144 100 36 4 152.1103 87.11049 18.77749 11.11089 7.111289 13.44469 32.11149 58.77829 93.44509 36 81 121 The formula for calculating the standard deviati on is 阿(532) 532 /66.5 = 8.154753 s8.154753 Therefore, the standard deviati on is s. -8.154753 The formula for calculating the standard devi ati on is (474) 474 - V59.25 7.697402 7.697402 Therefore, the stan dard deviati on is s, 7.697402

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The Interpretation of the coefficient of determination,$R^2$:

The value of the coefficient of determination of the scatter plot of the simple linear regression line is $R^2=97.95$ indicates that the percentage of the variation in the dependent variable (Y) can be explained by the independent variable Year (X). The percent of the year-to-year variation in scores is explained by the linear trend.