Question

The following data represent the time between eruptions and the length of eruption for 8 randomly selected geyser eruptions. Complete parts (a) through (c) below. Click here to view a scatter plot of the data. Click here to view a residual plot of the data. Time, x 12.15 11.62 11.96 12.19 11.29 Length, y 1.86 1.74 1.81 1.93 1.67 Time, x 11.68 12.13 11.59 11.68 Length, y 1.78 1.85 1.75 1.71 (a) What type of relation appears to exist between time between eruptions and length of eruption? X 0 Scatter plot of eruption data. Х Residual plot of eruption data. - A. Linear, positive association O B. Linear, negative association OC. A nonlinear pattern. Residuals vs. Time Time between Eruptions vs. Length of Eruption a OD. No association. 2.00 (b) Does the residual plot confirm that the relation between time between eruptions and length of eruption is linear? Q 1.90- 1.80 O A. No. The plot of the residuals shows no discernible pattern, implying that the explanatory and response variables are not linearly related B. Yes. The plot of the residuals shows no discernible pattern, so a linear model is appropriate. O C. Yes. The plot of the residuals shows a discernible pattern, implying that the explanatory and response variables are linearly related. OD. No. The plot of the residuals shows that the spread of the residuals is increasing or decreasing, violating the requirements of a linearn Residual 0.101 0.08 0.06 0.04- 0.02 0.00+ -0.02- -0.04- -0.06- -0.08 -0.10+ 11 Length 1.70- . 1.60 (c) The coefficient of determination is found to be 88.7%. Provide an interpretation of this value. 1.50- 11 11.4 12.2 12.6 11.4 12.2 12.6 11.8 Time 11.8 Time The least squares regression line explains % of the variation in (Type an integer or a decimal. Do not round.) Print Done Print Done Enter your answer in the answer box and then click Check Answer.

Answer 1

Solution-

c)

Coefficient of determination is 88.7%

So,

The least squares line explains 88.7% of variation in Length(response variable).

coefficient of determination means proportion of variation in 'y' explained by 'x'