Open Practice Tests

Tables and regression — Topic practice

5 exercises · 2 automatically checked · 3 written self-checks · Untimed

Instructions and review guidance

2 questions · Shuffled order · Untimed practice

Try each question before choosing Check answer. Guide question labels stay the same when you shuffle the bank. 3 written responses appear below the bank, with model answers for self-review; these are not automatically graded. Follow any rounding instruction in the question.

Guide question labels stay the same when the order changes. Check answers when you are ready to review.

Written self-checks are below the question bank and are excluded from the automatic score.

Written responses are self-review exercises.

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Compare the reasoning as well as the answer. Equivalent valid methods are welcome. A referenced example provides a targeted repair route.

The drill

Question 3

  • Guide question E3.3

The values 1, 4, and 7 occur with frequencies 2, 3, and 1, respectively. Find the mean of all six observations.

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Question 4

  • Guide question E3.4

An exact exponential model has outputs 80, 40, and 20 at times 0, 3, and 6. What does the model predict at time 9?

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

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Written self-checks

Write your complete response before opening the model answer. Compare both your answer and your reasoning.

Guide question E3.1

For f(x) = x2 − 2x + 3, make a two-row table for x = −1 and x = 2.

Show model answerHide model answer for question E3.1

f(−1) = 6 and f(2) = 3.

Define f(x)=x^2-2*x+3. Enter −1 and 2 in the input column and use a computed output column f(x_1). The outputs are 1 + 2 + 3 = 6 and 4 − 4 + 3 = 3. Preserve row correspondence: swapping outputs would describe different ordered pairs. Review Example 3.01.

Guide question E3.2

Fit a least-squares line to the data (0, 1), (1, 4), (2, 4), and (3, 7). Use that fitted line to predict the output at x = 4.

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8.5.

With the pairs in columns x1, y1, use y_1~m*x_1+b. The fitted line is y = 1.8x + 1.3, which predicts 1.8(4) + 1.3 = 8.5. This is a fitted prediction, not an observed value. As a check, the line passes through the mean point (1.5, 4) because 1.8(1.5) + 1.3 = 4. Review Example 3.05.

Guide question E3.5

A quadratic y = ax2 + bx + c passes through (0, 2) and (1, 5). Is its value at x = 2 determined uniquely? Justify your answer.

Show model answerHide model answer for question E3.5

No.

The first point fixes c = 2, while the second gives a + b = 3. Both x2 + 2x + 2 and 2x2 + x + 2 satisfy the two points, but their outputs at 2 are 10 and 12. The data do not identify a unique three-parameter quadratic. A regression display cannot create the missing condition. Review Example 3.14.