101B_hw_4_answers_W12steven

16 122 0 03 145end of harvest 178680 rain 0 08 314

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Unformatted text preview: nce is adolescent’s interest in physical science because among all of the predictors it has the highest standardized coefficient or beta weight. Q uestion five. Problem three from c hapter five section 5.4 a ) S how that the coefficient of the interaction term in model (5.10) i s statistically significant. In other words, show that the rate of c hange in quality rating depends on whether they have been w anted or unwanted. B ased on the R o utput Q uality^ = 5.16 122 – 0 .03 145*end of harvest + 1.78680 *rain – 0 .08 314 endofharvest*rain R ain is a dummy variable unwa n ted rain at the end of harvest = 1 Based on the R output the interaction between rain with end of harvest is statistically significant (t = -2.631, P = 0.012). This implies that the quality of vintage depends on whether there has been rain at harvest or not. As the interaction plot indicates, in the case of unwanted rain the quality of vintage decreases sharply (from 4.5 to 1; with one being the worst and five being the best) as a function of days since August 31st . Whereas, when there is no unwanted rain at the end of harvest, the quality of vintage does not change that much (range of values 3.5 to 4.5). b) e stimate the number of days of delay to the end of harvest it t akes to describe the quality of rating b y one point where there is No unwanted rain in the harvest Some unwanted rain in the harvest No unwanted rain in the harvest Quality^ = 5.11226 – 0.03145*end of harvest For end of harvest = 0, Quality = 5.11225 If we decrease quality by one point then we have 4.11226 4.11226 = 5.11226 -0.03145*end of harvest end of harvest = -1/-0.3145 = 31.79 Interpretation. In the cased of no wanted rain, if the quality rating is decreased by one point, the estimated number of days of delay to the end of harvest is around 32. Some unwanted rain at the end Q uality^ = 5.16122 + 1.78680*rain +( - 0.03145 - 0 .08314)* endofharvest*rain Qulaity^ = 6.9472 – 0.11459*end of harvest If we lower quality^ by one point = 5.9472 5.9472 = 6.9472 – 0.11459*end of harvest End of harvest = -1/-0.11459 = 8.7 So in the case of some unwanted rain, if we decrease the quality of vintage by one point, the estimated number of delays to the end of harvest is around nine days....
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This note was uploaded on 02/05/2014 for the course STAT 101A taught by Professor Mahtashesfandiari during the Fall '11 term at UCLA.

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