Question

Research Scenario: "By using words per sentence and characters per words, we can create formulas for the Flesch-Kincaid grade level readability. The readability statistics for random pages from a Harry Potter novel are given below." J.K. Rowling's "Harry Potter and the Sorcerer's Stone" Words/Sentence 15. 7 9 16.3 14.5 9.7 Characters/Word 4.1 4.2 | 4.2 4.4 4.3 Tir Grade Level 5.2 3.7 6.1 4. 9 4 .4 7.4 4.2 3.2 | 14 4.5 5.6 16.1 4.5 6.9 13.9 4.3 5.7 12.5 4. 4.1 17.2 4.4 6.7 11.5 4.3 4.4 Question: What is the correct analysis statement for the coefficient of determination between words per sentence (x-variable) and characters per word (y-variable)? 1.5% of the variance in characters per word is accounted for by words per sentence. 8% of the variance in characters per word is accounted for by words per sentence. 10% of the variance in characters per word is accounted for by words per sentence. 31% of the variance in characters per word is accounted for by words per sentence. O None of these

Answer 1

We input the given data set in R programming software and use the lm(.), cor(.) and summary(.) functions to answer the questions given here.

(i) The R-squared value is 0.10. Hence, 10% of the variance in characters per word is accounted for by words per sentence.
(ii) Here, x = Words/Sentence, y = F-K Grade level. The regression equation is: $\hat{y}$ = 0.680 + (0.334) . Now, for x = 10, predicted value of y = 0.680 + (0.334 * 10) = 4.022 = 4.
(iii) Now, x = Characters/Word, y = F-K Grade level. The slope in the regression equation is = 4.305. Hence, answer is True.
(iv) Correlation between Words/Sentence and Characters/Word = 0.312. Hence, the correlation is moderate and positive.
(v) Correlation between Words/Sentence and F-K Grade level = 0.905. Hence, the correlation is strong and positive.