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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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- 4.For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 33.88, Σγ^2 = 57365692 (b)Find the fitted regression line of the price of laptop on processor speed. (c) Find the predicted price of the laptop (y) for the processor speed x-1.9. (d) Compute the coefficient of determination and comment.The following estimated regression equation based on 10 observations was presented. ŷ = 25.1270 + 0.5309x1 + 0.4920x2 Here, SST = 6,738.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0563. Perform a t test for the significance of β1. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 > 0 Ha: β1 ≤ 0 b. H0: β1 ≠ 0 Ha: β1 = 0 c. H0: β1 < 0 Ha: β1 ≥ 0 d. H0: β1 = 0 Ha: β1 > 0 e. H0: β1 = 0 Ha: β1 ≠ 0 5. Find the value of the test statistic. (Round your answer to two decimal places.) 6. Find the p-value. (Round your answer to three decimal places.) p-value = 7. State your conclusion. a. Do not reject H0. There is sufficient evidence to conclude that β1 is significant. b. Reject H0. There is insufficient evidence to conclude that β1 is significant. c. Reject H0. There is sufficient evidence to conclude that β1 is significant. d. Do not reject H0. There is insufficient evidence to conclude that…The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,801 and 1,758, respectively. (a)Compute R2. (Round your answer to three decimal places.) R2 = (b)Compute Ra2.(Round your answer to three decimal places.) Ra2 = (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation provided a good fit as a…
- The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,807 and 1,757, respectively. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation did not provide a good…The following estimated regression equation based on 10 observations was presented. ŷ = 29.1260 + 0.5306x1 + 0.4680x2 The values of SST and SSR are 6,728.125 and 6,215.375, respectively. (a) Find SSE. SSE = (b) Compute R2. (Round your answer to three decimal places.) R2 = (c) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (d) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation.The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,808 and 1,780, respectively. (a) Compute R2. (b) Compute Ra2. (c) Comment on the goodness of fit.
- The following estimated regression equation based on 10 observations was presented ŷ = 25.1270 + 0.5309x1 + 0.4920x2 Here, SST = 6,738.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0563. Compute MSR and MSE. (Round your answers to three decimal places.) Compute F and perform the appropriate F test. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 ≠ 0 and β2 ≠ 0 Ha: One or more of the parameters is equal to zero. b. H0: β1 = β2 = 0 Ha: One or more of the parameters is not equal to zero. c. H0: β1 > β2 Ha: β1 ≤ β2 H0: β1 < β2 Ha: β1 ≥ β2 d. H0: β1 ≠ 0 and β2 = 0 Ha: β1 = 0 and β2 ≠ 0 2. Find the value of the test statistic. (Round your answer to two decimal places.) 3. Find the p-value. (Round your answer to three decimal places.) p-value = 4. State your conclusion. a. Reject H0. There is sufficient evidence to conclude that the overall model is significant. b. Do not reject H0. There…The exercise involving data in this and subsequent sections were designed to be solved using Excel. The following estimated regression equation is based on 10 observations was presented. yhat=29.1270+.5906x1 +.4980x2 Here SST=6,670.625 , SSR= 6,055.125 ,SB1= .0889 , and sb2=.0521. a. Compute MSR and MSE (to 3 decimals). b. Compute the F test statistic (to 2 decimals). Use F table. What is the p-value? - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 4 At a =.05 , what is your conclusion? - Select your answer -The overall model is significantThe overall model is not significantItem 5 c. Compute the t test statistic for the significance of Beta1 (to 2 decimals). Use t table. The p-value is - Select your answer -less than .01between .01 and .02between .02 and .05between .05…The following estimated regression equation based on 10 observations was presented. ŷ = 29.1670 + 0.5902x1 + 0.4960x2 Here, SST = 6,734.125, SSR = 6,212.375, sb1 = 0.0816, and sb2 = 0.0569. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR=?? MSE=?? (b) Compute F and perform the appropriate F test. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. H0: ?1 > ?2 Ha: ?1 ≤ ?2 H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) F = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that the overall model is significant. -Do not reject H0.…
- The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.The following estimated regression equation is based on 10 observations was presented. ŷ = 29.1270 + 0.5906x1 + 0.4980x2 . Here SST=6,724.125 , SSR = 6,216.375 , sb1 = 0.0813, sb2 = 0.0567. Compute MSR & MSE to 3 decimals, then compute F using the appropriate F test (round answer to 3 decimals). Use α = 0.05.Use the following set of points to test the null hypothesis =:H0β10 versus <:H1β10 . Use the P -value method with the =α0.10 level of significance. The slope of the regression line for this data is computed to be =b1−0.46482 , and the standard error of b1 is computed as =sb0.256636 . Use the TI- 84 calculator. x 14 14 4 16 21 14 15 9 y 17 14 19 9 10 10 9 10 t-score= p-value=