Please answer all!!!! a conditional probability.

$13.$ Heteroscedasticity of residuals in regression suggests that there is

a$.$ lack of independence in successive errors.

b$.$ non$-$constant variation in the errors.

c$.$ multi$-$collinearity among the predictors.

d$.$ non$-$normality in the errors.

$14.$ Which is a characteristic of the trimmed mean as a measure of center?

a$.$ It does not require sorting the sample.

b$.$ It is basically the same as the midrange.

c$.$ It is especially helpful in a small sample.

d$.$ It is similar to the mean if there are offsetting high and low extremes.

$15.$ A fitted multiple regression equation is $Y=12+3x_1-5x_2+7x_3+2x_4.$ When $x_1$ increases $2$ units and $x_2$ increases $2$ units as well, while $x_3$ and $x_4$ remain unchanged, what change would you expect in your estimate of $Y?$

a$.$ Decrease by $2$

b$.$ Decrease by $4$

c$.$ No change in $Y$

d$.$ Increase by $2$

$16.$ A sample of $16$ ATM transactions shows a mean transaction time of $67$ seconds with a standard deviation of $12$ seconds. State the hypotheses to test whether the mean transaction time exceeds $60$ seconds.

a$.H_0$:$60,H_1$:$>60$

b$.H_0$::$=60$

c$.H_0$:$=60,H_1$:$60$

d$.H_0$:$60,H_1$:$<mn\; id="EditorElement\_1439115">6</mn><mn\; id="EditorElement\_1439116">0</mn>$

$17.$ In the population model $y_i={}_0+{}_1{x}_i+{}_1,{}_0$ and ${}_1$ are

a$.$ statistics.

b$.$ parameters.

c$.$ observable.

d$.$ estimated.

$18.$ The variable used to predict another variable is called the

a$.$ dependent variable.

b$.$ independent variable.

c$.$ regression variable.

d$.$ response variable.

$19.$ Mary used a sample of $68$ large U$.$S$.$ cities to estimate the relationship between Crime $($annual property crimes per $100,000$ persons$)$ and Income $($median annual income per capita, in dollars$).$ Her estimated regression equation was Crime $=428+0\mathrm{.}050$ Income. If Income decreases by $1000,$ we would expect that Crime will

a$.$ increase by $428.$

b$.$ increase by $500.$

c$.$ decrease by $50.$

d$.$ remain unchanged.

$20.$ Which of the following is not a characteristic of the $t$ distribution?

b$.$ It is a symmetric distribution.

a$.$ It has a mean of $0.$

d$.$ It is a continuous distribution.

at annroaches $z$ as degrees of freedom decrease.