X =Lot &amp; Y =CostGive a broken line linear model with a breakpoint at 250: Y = B 0 + B 1 X 1 + B 2 X 2 + B 3 X 3 + ewhere X 2 = 0 or 1 depending on whether the lot size is ≥ 250 or &lt; 250 and X 3 = X 1 ⋅ X 2 ..Which hypothesis statement is equivalent to the statement: The two regression lines have the same intercept term? H 0 : B 0 = 0 H 0 : B 1 = 0 H 0 : B 2 = 0 H 0 : B 3 = 0 B 0 is obviously the intercept for simple linear regression models, however, the broken line phrasing is causing me to be confused on this. My initial instinct was to assume B 0 hypothesis was appropriate, but now I'm wondering if B 2 = 0 makes more sense.

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X  =Lot &amp;amp;   Y  =CostGive a broken line linear model with a breakpoint at   250:  Y  =      B    0    +      B    1        X    1    +      B    2        X    2    +      B    3        X    3    +  ewhere       X    2    =  0 or   1 depending on whether the lot size is   ≥  250 or   &amp;lt;  250 and       X    3    =      X    1    ⋅      X    2    ..Which hypothesis statement is equivalent to the statement: The two regression lines have the same intercept term?      H    0    :      B    0    =  0        H    0    :      B    1    =  0        H    0    :      B    2    =  0        H    0    :      B    3    =  0      B    0    is obviously the intercept for simple linear regression models, however, the broken line phrasing is causing me to be confused on this. My initial instinct was to assume       B    0   hypothesis was appropriate, but now I&#039;m wondering if       B    2    =  0 makes more sense.

Darion Sexton · Accepted Answer

Presumably       X    1   is the lot sizeWhen       X    1    &amp;lt;  250 you have       X    2    =  0 and       X    3    =      X    1        X    2    =  0 so-   Y  =      B    0    +      B    1        X    1    with intercept       B    0  When       X    1    ≥  250 you have       X    2    =  1 and       X    3    =      X    1        X    2    =      X    1   so-   Y  =  (      B    0    +      B    2    )  +  (      B    1    +      B    3    )      X    1    with intercept       B    0    +      B    2  so the intercepts are equal when       B    2    =  0

X = Lot & Y = Cost Give a broken line linear model with a breakpoint at 250 : Y

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