Question

Simple linear regression. An engineer used a random sample of n = 8 observations on a response variable, y, and a predictor variable, x, to estimate a simple linear regression model. The observations are given in the table below, together with some quantities calculated from the data and the model fit. xi: 6, 5, 4, 3, 7, 8, 9, 10 yi: 7.7, 6.6, 6.3, 3.7, 11.6, 11.4, 11.2, 14.1 x? = 6.5, y? = 9.075, Sxx = 42, SST = Syy = 86.155, SSE = 6.611 Use the sample quantities to answer the following questions. (a) Estimate the intercept ?? and slope ?? regression coefficients. (b) Write the estimated regression line equation and interpret it. (c) Estimate for the variance of the error term, ??². (d) Compute the coefficient of determination R² and explain the meaning of its value.

          Simple linear regression.

An engineer used a random sample of n = 8 observations on a response variable, y, and a predictor variable, x, to estimate a simple linear regression model. The observations are given in the table below, together with some quantities calculated from the data and the model fit.

xi: 6, 5, 4, 3, 7, 8, 9, 10
yi: 7.7, 6.6, 6.3, 3.7, 11.6, 11.4, 11.2, 14.1

x? = 6.5, y? = 9.075, Sxx = 42, SST = Syy = 86.155, SSE = 6.611

Use the sample quantities to answer the following questions.

(a) Estimate the intercept ?? and slope ?? regression coefficients.

(b) Write the estimated regression line equation and interpret it.

(c) Estimate for the variance of the error term, ??².

(d) Compute the coefficient of determination R² and explain the meaning of its value.

Simple linear regression.

An engineer used a random sample of n = 8 observations on a response variable, y, and a predictor variable, x, to estimate a simple linear regression model. The observations are given in the table below, together with some quantities calculated from the data and the model fit.

xi: 6, 5, 4, 3, 7, 8, 9, 10
yi: 7.7, 6.6, 6.3, 3.7, 11.6, 11.4, 11.2, 14.1

x? = 6.5, y? = 9.075, Sxx = 42, SST = Syy = 86.155, SSE = 6.611

Use the sample quantities to answer the following questions.

(a) Estimate the intercept ?? and slope ?? regression coefficients.

(b) Write the estimated regression line equation and interpret it.

(c) Estimate for the variance of the error term, ??².

(d) Compute the coefficient of determination R² and explain the meaning of its value.

Added by Katie P.

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