Q5). Show that in a simple linear regression Σεί 0 (a). (). (X,Y) is a point on the fitted regression line. (d). Verify parts (a), (b), and (c) for the data in the folder "Regression and Corr...
please help! Following is a simple linear regression model: y = a + A + & The following results were obtained from some statistical software. R2 = 0.523 Syx (regression standard error) = 3.028 n (total observations) = 41 Significance level = 0.05 = 5% Variable Interecpt Slope of X Parameter Estimate 0.519 -0.707 Std. Err. of Parameter Est 0.132 0.239 Note: For all the calculated numbers, keep three decimals. Write the fitted model (5 points) 2. Make a prediction...
A simple linear regression of Y on X reveals that the slope b is 3; the standard deviation of X is 2; and the standard deviation of Y is 8. What is the correlation coefficient between X and Y? Show steps.
A scientist study the relation of x=salinity level and y=nitrate level. He fitted a simple linear regression of y on x and got the following ANOVA table. Analysis of Variance Table Source df SS MS F p-value X 1 64.496 64.496 0.0000 Residual 6 6.113 MSE and F-statistic are missing in the table, please fill in. What is his sample size n? What is y’s total variation? what is the sample standard deviation sy? If we know x...
Probability and Statistics 1. Linear Regression Given 4 data points: X Y 5 15 Use simple linear regression to estimate ßo and ß, for the best-fit line ỹ ß0 + ßqx Calculate these values: x | 7 | S | Spy | Bo | Big Sketch the regression line and the data points below
(Do this problem without using R) Consider the simple linear regression model y =β0 + β1x + ε, where the errors are independent and normally distributed, with mean zero and constant variance σ2. Suppose we observe 4 observations x = (1, 1, −1, −1) and y = (5, 3, 4, 0). (a) Fit the simple linear regression model to this data and report the fitted regression line. (b) Carry out a test of hypotheses using α = 0.05 to determine...
We were unable to transcribe this imageD. b. Does a simple linear regression model appear to be appropriate? Explain. ;the relationship appears to be curvilinear Yes c. Develop an estimated regression equation for the data that you believe will best explain the relationship between these two variables. (Enter negative values as negative numbers). Several possible models can be fitted to these data, as shown below x + X2 (to 3 decimals) What is the value of the coefficient of determination?...
2.25 Consider the simple linear regression model y = Bo + B x + E, with E(E) = 0, Var(e) = , and e uncorrelated. a. Show that Cov(Bo, B.) =-TOP/Sr. b. Show that Cov(5, B2)=0. in very short simple way
Show work please, Thanks! Question 3: The regression line equation for a set of data is given by y-hat = 2.3x+5 with n = 10. The mean value of y is 10.1 for the data set. Use a = 0.05. A. If the linear correlation coefficient is r=0.521, what is the best predicted y-value for x = 5? Justify for your answer. B. If the linear correlation coefficient is r = 0.972, what is the best predicted y-value for x...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
(13 points) Suppose you have a simple linear regression model such that Y; = Bo + B18: +€4 with and N(0,0%) Call: 1m (formula - y - x) Formula: F=MSR/MSE, R2 = SSR/SSTO ANOVA decomposition: SSTOSSE + SSR Residuals: Min 1Q Modian -2.16313 -0.64507 -0.06586 Max 30 0.62479 3.00517 Coefficients: Estimate Std. Error t value Pr(> It) (Intercept) 8.00967 0.36529 21.93 -0.62009 0.04245 -14.61 <2e-16 ... <2e-16 .. Signif. codes: ****' 0.001 '** 0.01 '* 0.05 0.1'' 1 Residual standard...