The constant term is not always needed in the regression equation. For example, many physical principles involve proportions, where no con- stant term is needed. In general, if the dependent variable should be 0 when the independent vari- ables are 0, then the constant term is not needed. Then it is preferable to omit Bo and use the model Y = B, x1 + B2.X2 + ... + Bekk + E. Here focus on the special case k = 1. a. Differentiate the appropriate sum of squares to derive the one normal equation for estimat- ing Bı.
b. Express your normal equation in matrix terms, X'XB = X'y, where X consists of one column with the values of the predictor vari- able.
c. Apply part (b) to the data of Example 12.32, using hp for y and just engine size in X.
d. Explain why deletion of the constant term might be appropriate for the data set in part (c).
e. By fitting a regression model with a constant term added to the model of part (c), test the hypothesis that the constant is not needed.

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the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

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c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.