1. A study concluded that there was a correlation between refined sugar consumpt
ID: 3173022 • Letter: 1
Question
1.
A study concluded that there was a correlation between refined sugar consumption (Calories per person per day) and annual rate of major depression (cases per 100 people) The following data was available from a graph.
Country Sugar consumption Depression rate
Korea 150 2.3
United States 300 3.0
France 350 4.4
Germany 375 5.0
Canada 390 5.2
New Zealand 480 5.7
a) Compute and interpret the correlation coefficient for this data set.
b) Compute r-square interpret.
c) Evaluate the
i. slope________
ii. the y-intercept = ______
iii. the equation of the regression line
d) Is it reasonable to conclude that increasing sugar consumption leads to higher rates of depression. Explain.
Explanation / Answer
from above
a0) correlation coefficient =Sxy/(SSx*SSy)1/2=0.9445 ; as it +ve and near to 1.
which reflect that depression rate increases with increase of sugar content
b) also R2=(0.9445)2=0.892
which provide proportion of variability explained by independent variable in dependent variable
c)here slop b1 =Sxy/Sxx=0.0114
and intercept =Ybar-B1*Xbar =0.3706
hence regression equation Yhat=0.0114X+0.3706
d) Yes as correlation coefficient shows a strong +ve relationship b/w increase of sugar and strength of depression
x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 150.00 2.30 36417.36 3.87 -286.61 2.085268 0.04610972 300.00 3.00 1667.36 1.60 -374.60 3.799905 0.63984731 350.00 4.40 84.03 0.02 46.10 4.37145 0.0008151 375.00 5.00 1167.36 0.54 271.87 4.657223 0.11749627 390.00 5.20 2417.36 0.87 360.02 4.828686 0.13787383 480.00 5.70 19367.36 2.05 681.88 5.857468 0.02479621 Total 2045.00 25.60 61120.83 8.95 698.67 0.96693844 mean 340.83 4.27 SSx Ssy SxyRelated Questions
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