High School

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1. A teacher asks students to identify their favorite reality television show. What type of measurement scale do the different television shows make up?

Select one:
a. Nominal
b. Ordinal
c. Ratio
d. Interval

2. Given the following bivariate data, compute the sum of squares to one decimal place.

\[
\begin{array}{c|c}
x & y \\
\hline
2 & 3 \\
4 & 5 \\
8 & 6 \\
8 & 15 \\
18 & 10 \\
12 & 21 \\
\end{array}
\]

3. A regression between foot length (response variable in cm) and height (explanatory variable in inches) for 33 students resulted in the following regression equation: \(\hat{y} = 10.9 + 0.23x\). One student in the sample was 73 inches tall with a foot length of 29 cm. What is the residual for this student?

Select one:
a. 1.31 cm
b. -1.31 cm
c. 0.00 cm
d. 29.00 cm

4. A regression equation for left palm length (y variable) and right palm length (x variable) for 55 college students gave an error sum of squares (SSE) of 10.7 and a total sum of squares (SSTO) of 85.2. The proportion of variation explained by x, \(R^2\), is

Select one:
a. 87.4%
b. 11.2%
c. 12.696%
d. 88.8%

Answer :

The answer to the first question is a. Nominal. The answer to the second and third questions are option a -1.31 cm and option a 87.5%, respectively

To compute the sum of squares, we need the mean of the data.

x: 2, 4, 6, 8, 10, 12, 18, 21

y: 3, 5, 8, 6, 8, 15, 10, 12

Mean of x = (2+4+6+8+10+12+18+21)/8 = 9.375

Mean of y = (3+5+8+6+8+15+10+12)/8 = 8.5

SSE = Σ(yi - ŷi)²

= (3 - 8.525)² + (5 - 9.002)² + (8 - 11.48)² + (6 - 10.336)²

+ (8 - 11.48)² + (15 - 19.556)² + (10 - 12.962)² + (12 - 15.898)²

= 127.98

The residual is given by:

residual = observed y value - predicted y value

= 29 - (10.9 + 0.23*73)

= -1.31 cm

The proportion of variation explained by x is:

R² = 1 - (SSE/SSTO) = 1 - (10.7/85.2) = 0.875 or 87.5% (approx.)

The answer to the first question is a, the second and third questions are option a and option a respectively.

To know more about mean refer to-

https://brainly.com/question/30112112

#SPJ11

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