f d) Of all the parents and grandparents, whose height correlates best with the
ID: 3224604 • Letter: F
Question
f
d) Of all the parents and grandparents, whose height correlates best with the student height?
f) What is the correlation coefficient of the father’s height vs student height?
g) Fit a regression model with student height as the dependent variable and father’s height as the explanatory variable.
h) Does the sign of the slope parameter surprise you? What does your model predict as the change in height for an additional inch of height in the father’s height?
i) What student height would you predict for a student whose father’s height is 70 inches?
j) What does the model tell about a student’s height whose father is 55 inches tall?
k) What is the estimate of the error variance?
l) What is the standard error for the slope parameter?
m) Construct and interpret a 1-sided 95% confidence interval for the slope parameter that provides an upper bound.
n) Test the alternate hypothesis that the slope parameter is not equal to zero. Is it clear that on average student height increases with father’s height?
o) Compute the ANOVA table and calculate R2 . Explain the interpretation of the coefficient of determination.
p) What is the sample correlation coefficient “r”? Show that the t-statistic calculated in terms of t = r(n-2)0.5/(1-r 2 ) 0.5 is equal to the ratio of the slope estimate with standard error.
Student Height Father Height Mother Height Paternal Grandfather Height Paternal Grandmother Height Maternal Grandfather Height Maternal Grandmother Height Gender 75 70 70 72 63 71 69 M 75 72 69 65 62 77 64 M 63 68 66 70 68 74 62 F 70 72 67 69 67 69 65 F 67 70 64 67 63 66 63 F 70 72 64 74 62 67 64 M 75 74 67 72 60 70 63 M 69 65 63 66 60 70 63 M 60 67 62 72 65 69 64 F 70 78 62 72 70 70 61 M 62 68 63 65 61 65 63 F 70 70 65 65 65 71 61 M 71 68 64 67 62 71 63 m 68 66 64 65 62 73 58 m 66 72 65 72 61 70 62 m 67 73 68 72 60 72 62 f 71 66 68 64 67 66 62 m 62 74 60 74 63 66 62 f 58 60 52 55 45 54 50 m 65 72 66 70 62 67 63 f 64 72 60 68 60 67 64 f 69 74 66 74 66 74 69 f 70 69 64 68 65 73 64 m 62 65 65 67 60 71 60 f 70 73 68 75 69 69 67 m 72 70 69 68 68 73 63 m 67 69 61 64 58 70 64 f 64 70 58 70 60 71 61 f 69 73 69 68 64 72 69 m 71 68 69 71 69 73 71 m 62 68 63 68 61 66 60 f 67 74 65 72 64 70 63 f 72 74 66 74 64 70 64 m 63 67 62 65 59 67 62 f 62 66 64 69 59 70 68 f 66 68 61 68 64 68 64 m 76 64 67 76 68 73 71 m 73 70 64 56 55 73 63 m 67 72 65 70 65 67 68 f 64 68 61 70 63 69 62 f 65 61 62 60 54 72 60 m 77 75 68 74 66 68 66 m 74 73 66 70 67 68 65 m 70 72 68 69 61 71 72 m 65 67 63 66 62 60 64 f 68 67 62 67 60 65 62 m 90 69 62 69 62 69 69 m 71 69 66 69 62 70 65 m 72 71 63 70 50 68 62 m 69 74 70 73 70 73 71 f 65 69 62 69 67 70 59 m 65 63 61 65 60 63 59 m 63 65 61 66 59 68 62 f 68 72 58 72 66 66 62 m 78 74 70 72 66 73 65 m 73 77 64 71 62 65 64 m 68 67 65 67 65 65 64 m 62 70 63 75 64 68 63 f 69 68 65 67 65 64 65 m 70 71 69 70 65 60 69 m 72 74 66 72 60 68 62 m 69 67 64 67 63 64 66 m 75 72 70 71 65 72 64 m 74 74 70 72 70 69 68 m 69 68 67 69 66 74 66 m 63 68 64 64 61 70 62 f 63 70 63 73 63 60 61 f 68 74 66 72 70 72 66f
Explanation / Answer
d) Correlation matrix
Mother height correlates with student height.
f)
correlation between father height and student heigth is 0.386
g)
Student height = 29.805 + 0.554*Father height.
h)
Positive relation. No it does not surprise as father height increases student heigth increases.
h)
Student height= 29.801+0.554* 70 = 68.58
Student Height Father Height Mother Height Paternal Grandfather Height Paternal Grandmother Height Maternal Grandfather Height Maternal Grandmother Height Student Height 1 Father Height 0.385859 1 Mother Height 0.529383 0.422868 1 Paternal Grandfather Height 0.238384 0.621128 0.395259 1 Paternal Grandmother Height 0.282393 0.441617 0.564002 0.600817 1 Maternal Grandfather Height 0.336642 0.237559 0.497839 0.207394 0.335244 1 Maternal Grandmother Height 0.491428 0.359229 0.649452 0.486762 0.530247 0.354284 1Related Questions
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