Consider the following estimated regression equation, based on 10 observations. ŷ = 29.1270 +0.5906x1 +0.4980x2 The values of SST and SSR are 6,724.125 and 6,216.375, respectively. a. Find SSE (to 2 decimals). b. Compute R² (to 3 decimals). c. Compute R (to 3 decimals).
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.The following estimated regression equation is based on 30 observations. ŷ = 18.3 + 3.9x1 − 2.2x2 + 7.5x3 + 2.5x4 The values of SST and SSR are 1,805 and 1,762, respectively. a. Compute R2 = (to 3 decimals). b. Compute Ra2 = (to 3 decimals).
- 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 = 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 is based on 30 observations. y=17.4 - 4.0x 1- 2.3x2 +7.3x32.9x4 The values of SST and SSR are 1,808 and 1,760, respectively. Compute R2 (to 3 decimals). Compute Ra2 (to 3 decimals). How good is the fit provided by the estimated regression equation?
- Use the following table to find the equation of the regression line, between x and y x312304y210342From the following data, determine if the data has a positive or a negative relationship with each other. Showcase the regression line, and determine if the data provided fits the approximate curve. Use the formula attached together with the given data.The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
- 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.…Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.) answer: -4.5 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? answer:3.6 Suppose x2 increased by 2 units. What would be the expected change in x1? answer: 7.2 Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.461. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t 7.81 t critical ±A set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. Which is the regression equation for predicting Y from X?