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Part $1$

A multiple regression includes two$$ regressors:

Upper Y Subscript i equals beta $0$ plus beta $1$ Upper X Subscript $1$ i Baseline plus beta $2$ Upper X Subscript $2$ i Baseline plus u Subscript iYi$=$$0+$$1$X$1$i$+$$2$X$2$i$+$ui

Use the tool palette to the right to answer the following questions.

Part $2$

What is the expected change in Y if

Upper X $1$X$1$

increases by

$22$

units and

Upper X $2$X$2$

is$$ unchanged?

The expected change in Y if

Upper X $1$X$1$

increases by

$22$

units and

Upper X $2$X$2$

is unchanged is

$2$ times beta $12$$1.$

$($Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts.$$ E$.$g$.,$ a subscript can be created with the$\_$ character.$)$

Part $3$

What is the expected change in Y if

Upper X $2$X$2$

decreases by

$55$

units and

Upper X $1$X$1$

is$$ unchanged?

The expected change in Y if

Upper X $2$X$2$

decreases by

$55$

units and

Upper X $1$X$1$

is unchanged is

negative $5$ times beta $25$$2.$

$($Properly format your expression using the tools in the$$ palette.$)$

Part $4$

What is the expected change in Y if

Upper X $1$X$1$

increases by

$77$

units and

Upper X $2$X$2$

decreases by

$99$

$$units$?$

The expected change in Y if

Upper X $1$X$1$

increases by

$77$

units and

Upper X $2$X$2$

decreases by

$99$

units is

enter your response here.

$($Properly format your expression using the tools in the$$ palette.$)$