Assignment 1 FINAL

# As can be seen from the histogram it looks

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As can be seen from the histogram, it looks approximately normal although it is starting to look a little positively skewed which could be a potential violation. We suggest that a larger sample size needs to be examined. The mean of the residuals add up to 0.0004 which is approximately zero so this required condition can be checked off. The next required condition that needs to be satisfied is that the standard deviation of ε has to be constant regardless of the value of x and the residuals should not be related to each other. To check this condition, we must draw a scatter plot by looking at the predicted values of ŷ and of the residuals (ε).

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As can be seen by the scatter plot, they are randomly dispersed. There is no heteroscedasticity so there is no violation and this required condition can also be checked off. As can be seen from the scatter plot, there is a potential outlier which could be because of an error in recording the value, maybe the point should not have been included in the sample, or perhaps the observation is invalid. This does need to be dealt with since it can easily influence the least squares line. C) At the 5% significance level, is there enough evidence of a linear relationship between annual profit and the number of rooms? Present the correct hypothesis, calculate the necessary statistics, and conclude the hypothesis testing. -By testing slope we can determine whether or not there is a relationship between annual profit and the number of rooms. -When testing slope, we look at the t- distribution Step 1: Null and Alternative Hypothesis H 0 : B 1 = 0 - no linear relationship H 1 : B 1 ≠ 0 - there is a linear relationship Step 2: Rejection Region If t > t (α/2, v) or if t < - t (α/2, v), then reject null hypothesis, where v=df n-2= 8 If t > t (0.025, 8) or if t < - t (0.025, 8), then reject null hypothesis If t > 2.306 or less than -2.306, then reject null hypothesis Step 3: Calculate t Test statistic t= b 1 – B 1 / s b1 s b1 = s ε / square root of (n-1) x s 2 x To calculate s ε, we need to know SSE. SSE= (n-1)[s 2 y-sxy 2 /s 2 x] = 9 [16.0644 – (31.8667 2 /825.3778)]= 133.5066 s ε = square root of SSE/n-2 = square root of 133.5066/8 = 4.0851 s b1 = 4.0851/ square root of (9)(825.3778) = 0.0474 t = 0.03860 – 0 / 0.0474 = 0.8143 Step 4: Conclusion Since 0.8143 is not greater than 2.306 or less than -2.306, we do not reject H 0 . At the
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• Spring '12
• n/a

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