Reading and grades 3.2 / The Fathom scatterplot below shows the number of books
ID: 3131766 • Letter: R
Question
Reading and grades 3.2 / The Fathom scatterplot below shows the number of books read and the English grade for all 79 students in the study. A least- squares regression line has been added to the graph. Interpret the meaning of the y intercept in context. The student who reported reading 17 books for pleasure had an English GPA of 2.85. Find this student's residual. Show your work. How strong is the relationship between English grades and number of books read? Give appropriate evidence to support your answer.Explanation / Answer
a)
The y intercept is the value of y when x = 0.
Hence, it is the predicted English grade (3.42) when there are 0 books read by a student.
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b)
As
y^ = 3.42 + 0.024x
then if x = 17,
y^ = 3.42 + 0.024*17 = 3.828
Hence,
Residual = y - y^ = 2.85 - 3.828 = -0.978 [ANSWER]
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c)
As r^2 = 0.083, then only around 8.3% of the variation in English grade is explained by the number of books read. Hence, the relationship between English garde and number of books read is weak.
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