The following data were collected for two related variables x and y. A scatterplot indicates a non-linear association. The data is linearised using a logx transformation and a least squares line is then fitted. The equation of this line isclosest to:

Question

BlackTom AI · Accepted Answer

First, consider the transformation described: a logx transformation is applied to x, and then a least-squares line is fitted to y versus log x. This means the model is of the form y = a + b log(x), where log is typically base 10 in many introductory analyses unless stated otherwise.

Option a: y = 7.04 + 3.86 log x
- This has an intercept around 7.0 and a positive slope close to 3.9, which matches the observed pattern: when log x is near 0 (x close to 1), y is near 7; as log x increases toward about 1 (x near 10), y increases toward ~11. This aligns well with the data trend.

Option b: y = −1.71 + 0.25 log x
- The intercept is far too small (negative), and the slope is much too shallow. With log x ranging roughly from 0 to 1, this would imply y changes by about 0.25, hardly capturing the observed rise from about 7 to ~11. This is inconsistent with the data pattern.

Option c: y = 0.37 + 7.52 log x
- Here the intercept is near 0.37, which would place y near 0.37 when log x is 0 (x = 1). However the actual y at x = 1 is 7, so this intercept is clearly implausible given the data. Moreover, a slope as large as 7.52 would imply very steep growth as log x increases, which would overestimate y for larger x compared to the observed values.

Option d: y = 7.52 + 0.37 log x
- This has a plausible intercept around 7.5, which could align with y near 7 when x ≈ 1. However, the slope is only 0.37, which would yield a very small increase in y across the log x range (0 to about 1), predicting y around 7.4 to 7.9, far below the observed values near 11 as x grows. This underestimates the growth shown in the data.

In summary, option a provides a reasonable intercept near 7 and a slope near 3.9, which together reproduce the gradual, substantial increase in y as log x increases from 0 to about 1, matching the observed y-values across x = 1 to 11. The other options either place the line too low or too high, or assign an implausible rate of increase that disagrees with the data pattern.

The following data were collected for two related variables x and y. A scatterplot indicates a non-linear association. The data is linearised using a logx transformation and a least squares line is then fitted. The equation of this line isclosest to:

View Explanation

Log in for full answers

Similar Questions

Consider the following estimated regression model [math: ln⁡(yi)^=0.034−0.023xi]\widehat {\ln (y_i)}=0.034-0.023x_i where [math: ln⁡(.)]\ln (.) denotes the natural log. Which of the following is a correct interpretation?[Fill in the blank]

An exponential model with a quarterly data forecasting equation is log( ˆ Y i)=2.0886+0.0016Xi−0.0528Q1−0.0389Q2−0.0449Q3 Where Xi represents the coded quarter, Qi is a dummy variable for quarters, Qi=1 if it is ith quarter. What is the prediction when Xi=27, and it is the fourth quarter?

The following data were collected for two related variables x and y. A scatterplot indicates a non-linear association. The data is linearised using a logx transformation and a least squares line is then fitted. The equation of this line isclosest to:

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler