1. Consider the normal linear regression model Y~ N(a + Bx, o²). Data pairs (xi, yi) of sample size n= 43 have been collected and summarised below: n n n n n Σ |xi = 11.3, Σw = 154.8, Σy = 19.2, Σy =135, & Σαϊy = 24.9. i=1 i=1 i=1 i=1 i=1 From this data, compute the least-squares estimates for a and ß. Given that the residual variance estimate is s² = 0.0544, evaluate the expected value and 95% prediction interval a future response Yo at x = 10. Clearly state the definitions/formulas you are using in this question and report the pre- dicted value and interval correct to 2 decimal places. From the given information, provide a brief comment about this prediction.

The temperatures (Observed and Expected) in centigrade for certain concrete mix sample have been presented as shown in the table below: Observed Expected Frequency Frequency 9 10 19 21 27 25 29 27 20 24 16 21 8 10 a- Use the data above to determine the Correlation Coefficient, between the Expected and the Observed frequencies b- Use the data above to determine the equation of the regression line between the expected and the observed frequencies. Note: Let the Observed values represent X and the Expected values represent Y.

After you estimate a simple linear regression you obtain the following sample regression function: Y₁ = 8.8 +0.7091 Xį With an r² of 0.784. The observed dependent variable used for the regression is: Y 9 675 40 40 40 6 5 5 5 5 1 1 Compute the sample variance of X? 8.45 10.79 9.17 7.19 Cannot be computed with the provided information.

Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.

2. We performed a linear regression using 25 observations. From the regression output we find that bo = 5.7, bị = 12.9, x = 11.4, Sz = 3.2 and MSE = 12.25. a. From the least squares line, what is the predicted response when x* = 10.65? y = b. What is the 95% confidence interval for the mean response when x* = 10.65? c. What is the 95% prediction interval for an individual response when x* = 10.65? d. Which interval is wider? The confidence interval or the prediction interval? O a. Confidence Interval b. Prediction Interval

The least-square regression line for the given data is y = 0.449x - 30.27. Determine the residual of a data point for which x = 98 and y = 15, rounding to three decimal places. Temperature, x Number of absences, y OA. 28.732 B. 1.268 C. 121.535 O D. 13.732 72 3 85 7 91 10 90 10 88 98 75 100 80 8 15 4 15 5

i)Test individually whether the slope coefficients are significant at 10% significance level. ii)Test the overall significance of the estimated regression at 1% significance level.

Given the table below, Let y, x1, x2, and x3 be the time of concentration (t, in hr), watershed length (L in ft), watershed slope (S in %), and runoff curve number (CN): Evaluate the linear multiple regression model with two or three predictor variables. Compute the multiple correlation coefficient, the standard error of estimate, and the standard deviation of the variable y. Discuss the reliability of the model