Linear relationship between x and y Nonlinear relationship between x and y Norma
ID: 3317034 • Letter: L
Question
Linear relationship between x and y
Nonlinear relationship between x and y
Normally distributed y's for each x
Non-normally distributed y's for each x
Standard deviations of the y's are constant for each x
Standard deviations of the y's are not constant for each x
(b) Given that the assumptions are satisfied, what is the p-value to test for a significant negative linear relationship between years and ice breakup date?
-1.6640
0.0000
0.1097
0.0549
0.9451
(c) Assuming that there is a significant linear relationship between year and breakup date, what is the mean breakup date predicted by the estimated regression line for the year 1935? (Plug 35 into the equation)
-134.386 -0.266(35) = -143.696
134.386 + 0.266(35) = 143.696
134.386 -0.266(35) = 125.076
0.266 + 134.386(35) = 4703.776
-0.266 + 134.386(35) = 4703.244
(d) The actual breakup date for 1935 was 135.5642. What is the residual for this point?
-10.49
-5.24
0.00
10.49
20.98
(e) The R2 for this simple linear regression was 10.75%. Interpret what this value means.
10.75% represents the strength of the linear relationship between breakup date and year.
10.75% of all breakup dates lie exactly on the least-squares estimated line.
10.75% of the breakup dates can be explained by the year.
The percent of the variability in the year that can be explained by the linear relationship with breakup date is 10.75%.
The percent of the variability in the breakup date that can be explained by the linear relationship with year is 10.75%.
Explanation / Answer
a) Linear relationship between x and y
Normally distributed y's for each x
Standard deviations of the y's are constant for each x
b)
as it is one tailed test p vlaue =0.0549
c)
134.386 -0.266(35)=125.076
d) residual =actual -predicted =135.5642-125.076 =10.49
e)
The percent of the variability in the breakup date that can be explained by the linear relationship with year is 10.75%.
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