The SAT and the ACT are the two major standardized tests that colleges use to ev

Question

The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data479.dat gives the scores of 60 students who did this. How can we relate the two tests? (a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations. (b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.) ACT =_____+______ (SAT) t =? P =? (c) What is the correlation between the two tests? (Round your answer to three decimal places.)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: act
Independent Variable: sat
act = -4.3123114 + 0.026599615 sat
Sample size: 60
R (correlation coefficient) = 0.87623641
R-sq = 0.76779024
Estimate of error standard deviation: 2.5349039

Parameter estimates:

Analysis of variance table for regression model:

Hence,

b) Regression line:

ACT = -4.312 + 0.027 (SAT)

t = 13.85

P = 0.0000

c) Correlation = 0.876

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -4.3123114 1.7846799 0 58 -2.416294 0.0188 Slope 0.026599615 0.0019207918 0 58 13.848255 <0.0001

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