Chapter 2 HW

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Feb 20, 2024

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Ch 2 homework problems (5 points each) 2.122 Dwelling permits (dataset MEIS) A) The scatterplot is semi linear with a positive direction. The r value of 0.007054 shows the positive relationship and a moderately weak strength because the value is close to zero. The vast scatter of the plot with a probable outlier around Dwell Permit 300 shows more spread of the data and a larger residual. The large residual can be observed by the large standard error of the residuals and the large gaps between the calculated residual values. B) Sales=102.00489+0.03065(DwellPermit) C) The slope is 0.03065. The positive slope represents a positive correlation. D) The intercept of the line is 102.00489. This value is important in explaining the relationship of the two variables because it can be used in the equation y= b0 +b1X to help predict values for both the explanatory and response variables. The intercept can also be used further to determine if the regression line is a good fit for the data based on the number of data points that come into contact with it. The intercept line does not seem very favorable due to only 3 intercepts being on the regression line which is why this interpretation is probably not useful for the relationship between these variables. E) Sales=102.00489+0.03065(117.8) = 105.6154 F) Residual= (Observed-Predicted)= (117.8-105.615)= 12.185 G) .7% means this model is not a good fit for the data

Residuals: Min 1Q Median 3Q Max -70.383 -0.988 2.473 6.634 19.555 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 102.00489 12.36943 8.247 2.41e-07 *** DwellPermit 0.03065 0.08820 0.348 0.732 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 18.87 on 17 degrees of freedom Multiple R-squared: 0.007054, Adjusted R-squared: -0.05135 F-statistic: 0.1208 on 1 and 17 DF, p-value: 0.7325 > #Predict y when x=117.8 105.6154 > #find the residual (obs - pred)

2.130 Fields of study by country for college students (dataset FOS) A) Canada 176/4576= .03846= 3.8% France 672/4576= .1468= 14.7% Germany 218/4576= .04763= 4.8% Italy 321/4576= .07014= 7.0% Japan 645/4576= .1409= 14.1% UK 475/4576= .1038= 10.38% US 2069/4576= .4521= 45.2% B) In the US the highest number of students studying towards a degree specifically in special science, business, and law in comparison to other countries. France has the highest number of students studying for a degree in the other category. Except for France, all countries have their highest number of students studying towards a degree in special science, business, and law. After that, the second likely degree is by students studying science, mathematics, and engineering in all countries except the US which is arts and humanities. Canada France Germany Italy Japan UK US SsBL 64 153 66 125 250 152 878 SME 35 111 66 80 136 128 355 AH 27 74 33 42 123 105 397 Ed 20 45 18 16 39 14 167

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Other 30 289 35 58 97 76 272 Canada France Germany Italy Japan UK SsBL 0.3636364 0.22767857 0.30275229 0.38940810 0.38759690 0.32000000 SME 0.1988636 0.16517857 0.30275229 0.24922118 0.21085271 0.26947368 AH 0.1534091 0.11011905 0.15137615 0.13084112 0.19069767 0.22105263 Ed 0.1136364 0.06696429 0.08256881 0.04984424 0.06046512 0.02947368 Other 0.1704545 0.43005952 0.16055046 0.18068536 0.15038760 0.16000000 US SsBL 0.42435959 SME 0.17158047 AH 0.19188014 Ed 0.08071532 Other 0.13146448 2.140 Predicting text pages (dataset TEXTP) A) The scatterplot has a linear form and pattern. The positive r value of 0.926 shows a positive direction and strong correlation because of its closeness to 1. B) Text pages= -6.20176+ 1.20810(LaTexPages) C) Text pages= -6.20176+ 1.20810(52) = 56.6193 D) The regression line is based on the equation of Text pages= -6.20176+ 1.20810(LaTexPages). This equation was constructed by the y intercept of the line which is -6.20176 found with software and the

slope 1.20810 also calculated with software. I used these values and entered them into the equation of y= b0 +b1X and including the variables of of x and y in this data set text pages and LaTexPages. The regression line is drawn to best fit the plotted data and reached as many points as possible to accurately show a trend within the data and a useful mechanism to use to predict data values. Data values can be predicted by use the equation of the regression line and plugging in values for x to find the predicted y or even vice versa such as in this example Text pages= -6.20176+ 1.20810(52) = 56.6193. The percent variation of the line is 93.2% which shows a large r and a good fit for the model so you as the author can trust this model to have relevant predictions with the regression line equation. Residuals: Min 1Q Median 3Q Max -8.446 -4.654 -1.163 4.253 12.178 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -6.20176 5.71233 -1.086 0.301 LaTeXPages 1.20810 0.09828 12.292 9.08e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 6.332 on 11 degrees of freedom Multiple R-squared: 0.9321, Adjusted R-squared: 0.926 F-statistic: 151.1 on 1 and 11 DF, p-value: 9.08e-08

> #predict y when x=52 56.61937

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