ALEKS ReviewDictionar Calendar Business Stal Bivariate data obtained for the pai

Question

ALEKS ReviewDictionar Calendar Business Stal Bivariate data obtained for the paired variables x and y are shown below, in the table labelled Sample data. " These data are plotted in the scatter. plot in Figure 1, which also displays the least squares regression line for the data. The equation for this line is y=4.56-0.39x. In the "Calculations" table are calculations involving the observed y values, the mean y of these values, and the values from the regression equation. predicted Sample data Calculations mYTY 0.8 4.2 0.0023 0.7885 00918 0.0023 02275 0.7056 0.4096 0.3136 0 0256 0.5776 2.0320 0.1136 3.2 2.8 4.3 3.2 4.8 2.6 2621 co2a 0.1005 0.0077 07046 07 Columa 0.4863 1.5618 Figure 1 Answer the following: 1.For the data poln132. 2.8), the value ofthe residual is.(Round your answer to at least 2 decimal places.) 2. The least-squares regression line given above is said to be a ine which testes-the sample data. The term "best fits" is used because the ine has an equation that minimizes the 3. which for these data is t 3. The vanation in the sample yvalues that is not explained by the estimated linear relationship between r and yis gven by the ( , which for these data is ? 4. The propotion of the total variation in the sample yvalues that can be explained by the estimated linear relationship between x and yul·(Round your answer to at least 2 decimal places.)

Explanation / Answer

1. Here,

the linear regression line

y^ = 4.56 - 0.39x

y^(3.2) = 4.56 - 0.39 * 3.2 = 3.312

Residual = 2.8 - 3.312 = -0.512

Q.2

The linear regression fitted line minimizes the error sum of squares which is for these data is 0.4863

Q.3 the variation that is not explained by

Error sum of squares/ Total sum of squares * 100 = 0.4863 * 100 / 2.0320 = 23.932 %

is unexplained by which for these data is 0.2393

Q.4

The proportion that is total explined by linear relationship is

1.5618/ 2.0320 = 0.7607

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