1. (40 points) A Michigan travel agent wants to examine the relationship between
ID: 2909314 • Letter: 1
Question
1. (40 points) A Michigan travel agent wants to examine the relationship between the number of days temperatures exceed 40 degrees in December and the number of subsequent cruise bookings in January. Data from 10 years of bookings and temperatures were collected with the following results: Days with Temps Over 40 in December Scatter Plot of Bookings and Days with Temps Over 40 degrees Bookings in January 150 178 13 17 64 150 100 169 7 16 6 21 80 39 Multiple R R Square Adjusted R Square Standard Error Observations 0.91743195 0.841681382 0.821891555 26.85569546 ANOVA Regression Residual Total 1 30674.5729730674.57297 42.53101219 0.000183879 8 5769.827031 721.2283788 36444-4 Coefficients Standard Error 242.0644525 18.53797901 13.05775847 1.12345E-06 199.3157962 284.8131087 10.04340677 t Stat P- value Lower 95% Upper 95% Intercept X Variable 1 1.540026498 -6.521580498 0.000183879 -13.59471425 -6492099302 A. Based on the scatter plot for the data, does it appear that a positive, negative, or no linear relationship exists between number of days with temperatur cruise bookings in January? a. Positive relationship b. Negative relationship es above 40 in December and number of c. No relationshipExplanation / Answer
From the scatter plot it seems that there is a negative relationship between days with temperature over 40 and bookings in January because bookings decrease when days with temperature over 40 increases.
f. The regression equation from given data is
Bookings in January = 242.064 - 10.043 * days with temperature over 40 in December
g. The slope -10.043 is the change in the dependent variable (bookings in January) when there is a unit change in the independent variable (days with temperature over 40 in December).
h. the 95% confidence interval for slope is (-13.594 -6.492) which indicates that there are 95% chances that the slope of the regression line will remain within these limits and the negative sign of these limits indicates negative correlation. Clearly, 0 is not contained in the interval showing that the variables can never be uncorrelated.
i. The p-value for hypothesis test of slope is 0.00018 which is less than 0.05, thus the null hypothesis regarding slope (that is slope = 0) will be rejected.
j.bookings in January = 242.0644 - 10.0434 *10 = 141.63
k.Yes, the model produces an estimate which is close to actual value.
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