Let Z be a categorical variable with four levels: 1, 2, 3 and 4, and let X and Y be continuous. Using the following R output, estimate the average predicted value of Y in each category of Z when X is 10. ## ## ## Call: ## lm(formula = y - x * as. factor(z), data = d) ## ## Residuals: Min 1Q Median 3Q Max ## -4.0381 -1.7994 0.0844 1.8140 4.7927 ## ## Coefficients: Estimate Std. Error t value Pr>It!) ## (Intercept) 17.5027 40.2549 0.435 0.668 ## x 0.3116 10.4209 0.030 0.976 ## as. factor (z)1 27.2830 40.5103 0.673 0.507 ## as. factor(z)2 21.8574 40.3848 0.541 0.593 ## as. factor(z)4 10.2564 40.3781 0.254 0.802 ## x:as. factor (z)1 7.4968 10.5713 0.709 0.485 ## x:as. factor (z)2 5.6127 10.4778 0.536 0.597 ## x:as. factor(z)4 2.7892 10.4522 0.267 0.792 ## ## Residual standard error: 2.705 on 24 degrees of freedom ## Multiple R-squared: 0.844, Adjusted R-squared: 0.7985 ## F-statistic: 18.55 on 7 and 24 DF, p-value: 2.963e-08

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be