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is a linear relationship between the Number correct and the wmc which can be seen in the scatter plot above. However, while the two slopes of the different form of sentence inputs are very similar, the intercepts are different. c) It is not necessary to recode the particular categorical variable because there are only two levels to the categorical variable of visual versus auditory sentence input. Also it is not necessary because the variable is already in the indicator variable form of 0/1. d) The new variable is equal to zero for subjects 1-21. These subjects are the subjects who were given the visual sentence input.

e) Y’ = -.695 - 1.275 + 0.589
1.275 is the auditory form of sentence input, 0.589 is the working memory capacity and Y’ is the predicted value of the correct number of sentences.

f) Visual input: Y’ = 0.695 +0.589
Auditory input: Y’=0.695 – 1.275 +0.589

g) The p-value for the F-statistic 0.009 is 0.924 which is the p-value for comparing Model 1 and Model 2 which is also 0.924. Thus the simpler model is more efficient than the interaction model. This also shows that the linear relationships between number correct and wcm shown in the scatterplot are parallel. Therefore at each level of wcm, the mean difference between the forms of sentence input is the same.

h)
H0: (β_A ) ̂=0
Ha: (β_A ) ̂≠0
At every wcm, the number of correct identifications of the sentences is 1.275 lower for auditory input than for visual input. The lower CI was -2.133 and the upper CI was -0.418 The p-value of 0.005 shows that the null hypothesis should be rejected.

i)
H0: (β_wmc ) ̂=0
Ha: (β_wmc ) ̂≠0
There is a 0.589 point increase in number of words identified correctly for every unit rise in working memory capacity. The CI interval was (0.439, 0.739) and the p- value was 0.000. Thus the null hypothesis is rejected which shows an association between wmc and change in words correctly identified.

j)
H0: (β_0 ) ̂=0
Ha: (β_0 ) ̂≠0
The estimate...
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