Practice Quiz 2 Solution2

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Kennesaw State University *

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Statistics

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Feb 20, 2024

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1 Practice Quiz 2 Solution CASE 1 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 S b1 = 0.2683 1. Refer to Case 1. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is a. $66,000 b. $5,412 c. $66 d. $17,400 Answer: A Solution: ^ y =12 +1.8 *30=12+54=66 2. Refer to Case 1. The F statistic computed from the above data is a. 3 b. 45 c. 48 d. 50 Answer: B Solution : F statistic=MSR/MSE MSR=SSR/1 = SSR 1 SSR 1 , MSE= SSE/(n-2)= SSE n 2 ¿ ¿ SSE n 2 From our data n=17, n-2=15 MSR=225/1, MSE=75/15=5 F statistic=225/5=45 3. Refer to Case 1. To perform an F test, the p -value is a. less than .01
2 b. between .01 and .025 c. between .025 and .05 d. between .05 and 0.1 Answer: A Solution : F=45, df1=1, df2=n-2=17-2=15 p -value is FDIST (F, df1, df2)=FDIST(45,1,15)= 7.00656E-06 4. Refer to Case 1. The t statistic for testing the significance of the slope is a. 1.80 b. 1.96 c. 6.708 d. 0.555 Answer: C Solution : t statistic =b 1 /s b1 S b1 = 0.2683. It’s given Slope b 1 =1.8 t statistic=1.8/0.2683=6.708 5. Refer to Exhibit Case 1. The critical t value for testing the significance of the slope at 95% confidence is a. 1.753 b. 2.131 c. 1.746 d. 2.120 Answer: B Solution : t critical=TINV (α,df=n-2) For our question α=0.05, df=17-2=15 t critical =TINV(0.05,15)= 2.131449546 CASE 2 The following information regarding a dependent variable Y and an independent variable X is provided ΣX = 90 Σ (Y - )(X - ) = -156 ΣY = 340 Σ (X - ) 2 = 234 n = 4 Σ (Y - ) 2 = 1974 SSR = 104
3 1. Refer to Case 2. The total sum of squares (SST) is a. -156 b. 234 c. 1870 d. 1974 Answer: D Solution : SST = ( y i y ) 2 SST = 1974 SST=SUM (yi-y-bar)^2 2. Refer to Case 2. The sum of squares due to error (SSE) is a. -156 b. 234 c. 1870 d. 1974 Answer: C Solution : We know that SST = SSR + SSE 1974=104+SSE SSE=1974-104=1870 3. Refer to Case 2. The mean square error (MSE) is a. 1870 b. 13 c. 1974 d. 935 Answer: D Solution : MSE = SSE n 2 SSE n 2 n=4-2=2 MSE=1870/2=935 4. Refer to Case 2. The slope of the regression equation is a. -0.667 b. 0.667 c. 100 d. -100 Answer: A Solution : b 1 = ( x i x )( y i y ) ¿¿¿
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