Linear relationship between x and yNonlinear relationship between x and yNormall

Question

Linear relationship between x and yNonlinear relationship between x and yNormally distributed y's for each xNon-normally distributed y's for each xStandard deviations of the y's are constant for each xStandard deviations of the y's are not constant for each xFan shape in the residuals

(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?

-1.66400.0000    0.10970.05490.9451

(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) = -143.696134.386 + 0.266(35) = 143.696    134.386 -0.266(35) = 125.0760.266 + 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    0.0010.4920.98

(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%.

35 130 25 20 115 y 0.2663x 134.39 R 0.1075 110 t 22 27 32 37 Year Standard Coefficient t-Value p-Value Regression Table Error Constant 134.386 4.782 28.103 0.0001 Year 0.266 0.160 1.664 0.1097

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)

0.10970.05490.9451

c)

134.386 -0.266(35)=125.076

d)

135.5642-125.076=10.4882

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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