2015Spring-Exam2-Sample Exam Solutions

2015Spring-Exam2-Sample Exam Solutions - SAM PLE EXAM FOR i...

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Unformatted text preview: SAM PLE EXAM FOR i DT E R M 2 P ' I N sif'i...‘...":§::§i 2 O 1 5 “'- E Question 1 — Simple Linear Regression — Fruit Calories Dependent Variable: Calories Independent Variable: Sugar DATASET Fruit Sugar Calories Grapefruit 8 52 Kiwi 6 42 Banana 14 105 Avocado 1 234 Watermelon 17 85 Apple 19 95 Pineapple 89 452 Blueberry 15 85 Strawberry 0.6 4 Cantaloupe 43 186 1. Interpret multiple r. Calories and Sugar are 85% correlated. 2. Calculate r-square manually. interpret. 110475.91/153080272%. 72% of the variation in calories can be expiained by sugar. 3. Calculate standard error of the estimate manually. Would you prefer a lower or a higher standard error of 42604.09 10-1—1 4. Write the regression model. 31" 2 45.825 + 4.147(x) Interpret the intercept and slope coefficients. If you increase sugar by one gram, calories goes up by 4.147. When sugar is zero gram, calories is 45.825. 5. What happens to the calories if sugar increases by 10? Calories go up by 41.47. Find the predicted value of calories when sugar is 60. y = 45.825 + 4.147(60) : 294.67 8. Find the residual for the pineapple observation {In the first observation, sugar =89 and calories =452) y 2 45.825 + 4.147(89) = 414.95 452 — 414.95 = 37.05 the estimate? Why? = 72.98. We prefer lower because it means smaller residual. 5-" 7" mONH mmoa Dumd wwod mood mmmd Hfimd DES» 59% 3de 93.3. smmdfi nmmdm- n36 Hmma mmfidm mmmfiv 3855. &Q.mm Luau: wmodo. $33 fimm $9.95 wmmm EEO... mEEi Bum u Sim 95.0:ch flamUEmou owommfi m .32 Hm.mmmm 8633 m “gamma mfiood Show Emma: 3.333 a :ofimmtmwm a muccfiegm . m 3 mm he <>Oz< 0H mcozmimmno mods Btu 333.8% 8.0 238 m 83.33 Nnd Emzcm m mmd m 22:22 mutmtfim :ofimmkmmm .5950 >m<§§3m Question 2 — Randomized Block Design — Grocery Stores You want to decide whether there is a blocking effect. 0 Develop the hypothesis Ho: um= Elf-m- llc Ha: Not all the us are the same 0 Decide whether you reject the null using the test-statistic approach. Draw the F-distribution, show the RR/NRR and show where the F-stat falls (aipha=5%). Interpret your answer. Wm fir Si .33 (4‘ 3 gr? Reject the null. Blocking is significant. You should control for blocking and use randomized block design. 0 Decide whether you reject the null using the p-value approach. 0.00<0.05, reject You want to decide whether there is a significant difference in prices of goods in different grocery stores. 0 Develop the hypothesis Ho: lJ-WF: lJ-Gristede=l-1Fariway=ltlss Ha: Not all the us are the same 9 Decide whether you reject the null using the test-statistic approach. Draw the F-distribution, show the RR/NRR and show where the F—stat falls (alpha=5%). interpret your answer. Reject the null. The prices of products in different grocery store are different. 9 Decide whether you reject the null using the p-value approach. 0.01<0.05, reject Dataset Wm Item Whole Foods Gristede's Fairway Stop&Shop Half-gallon milk 2.19 1.59 1.35 1.89 Dozen eggs 2.39 1.59 1.69 2.29 Tropicana orange juice (64 oz.) 2 2.99 2.49 2 Head of Boston lettuce 1.98 1.49 1.29 1.29 Ground round 11b. 4.99 3.99 3.69 3.59 Bumble Bee tuna 6 oz. can 1.79 0.79 1.33 1.5 Granny Smith apples (1 lb.) 1.69 ' 1.99 1.49 0.99 Box DeCecco lingulni 1.99 1.5 1.59 1.79 Salmon steak 1 lb. 7.99 4.99 5.99 5.99 Whole chicken per pound 2.19 1.19 1.49 1.49 ANOVA Source of Variation SS df M5 F P-volue F crit Rows 87.39 9.00 9.71 42.56 0.00 2.25 Columns 3.45 3.00 1.15 5.04 0.01 2.96 Error 6.16 27.00 0.23 Total 97.00 39.00 Question 3 — 'i'wo Way ANOVA — Height of Teenagers You want to decide whether there is a significant difference in the height of teenagers based on gender. 0 Develop the hypothesis Ho: IJ-lil‘lale= ”Female Ha: Not all the us are the same 9 Decide whether you reject the nuil using the test-statistic approach. Draw the F—distribution, show the RR/NRR and show where the F-stat falls (alpha=5%). Interpret your answer. ................ first: {+153 litfi‘fi‘i Reject, There is a significant difference in the height of teenagers based on gender. 0 Decide whether you reject the null using the p-value approach. 0.00<0.05, reject You want to decide whether there is a significant difference in the height of teenagers based on the sports they are doing. 0 Develop the hypothesis Ho: ivtFootbai= “BasketbalIEUVolieyball Ha: Not all the us are the same Decide whether you reject the null using the test-statistic approach. Draw the F-distribution, show the RR/NRR and show where the F-stat falls (alpha=5%). Interpret your answer. Reject, There is a significant difference in the height of teenagers based on sports. 9 Decide whether you reject the null using the p-value approach. 0.01<0.05, reject Dataset Male Female Football 170 150 180 159 167 171 Basketball 189 178 191 175 179 180 Volleyball 168 155 184 163 183 168 ANOVA Source of Variation SS df MS F P~value F crit Sample 813.44 2 406.72 7.43 0.01 3.89 Columns 696.89 1 696.89 12.74 0.00 4.75 Interaction 44.11 2 22.06 0.40 0.68 3.89 Within 656.67 12 54.72 Total 2211.11 17 Question 4 - One Way ANOVA — Stock Returns of Utilities You want to find out whether there is a significant difference in stock returns of utiiities during the recession and normal economy. 0 Develop the hypothesis Ho: “Recession: “normal Ha: Not all the us are the same 0 Decide whether you reject the null using the test-statistic approach. Draw the F-distribution, show the RR/NRR and show where the F-stat fails (alpha=5%). Find F-test and F-critical manually. Interpret your answer. K _ Do 'not reject. There is no significant difference in stock returns of utilities during the recession and normal economy. - Decide whether you reject the null using the p—value approach. .59>0.05 do not reject. Dataset Recession Normal 1.2 1.1 1.15 1.34 0.6 0.8 0.3 0.35 0.85 1 -O.12 0.3 Anova: Single Factor SUMMARY Groups Count Sum Average Variance recession 6 3.98 0.66 026 normal 6 4.89 0.82 0.17 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.069 1 0.07 0.32 0.59 4.96 Within Groups 2.182 10 0.22 Total 2.251 11 ...
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