The regression model equation for your sample of data is Ŷi = 7.42 – 0.64Xi, as shown in the graph below.

When X equals 3, what can you say about the predicted value of the dependent variable Y (i.e., Ŷ)?

Question

The regression model equation for your sample of data is Ŷi = 7.42 – 0.64Xi, as shown in the graph below.

When X equals 3, what can you say about the predicted value of the dependent variable Y (i.e., Ŷ)?

BlackTom AI · Accepted Answer

First, translate the regression equation into a concrete prediction for X = 3. Substituting X = 3 into Ŷi = 7.42 – 0.64Xi gives Ŷ = 7.42 – 0.64 × 3.

Next, compute the multiplication: 0.64 × 3 = 1.92. Then perform the subtraction: 7.42 – 1.92 = 5.50.

Thus, the model predicts a Y value of 5.50 for X = 3. This falls between 5 and 6 on the Y-axis.

To evaluate the given option, consider what the statement asserts: that the predicted Ŷ is definitely between 5 and 6 for this sample. Since the calculation yields 5.50, which lies in that interval, the statement is consistent with the computed prediction.

Note: The exact predicted value is 5.50, not 5, 6, or any other discrete value. Saying it is between 5 and 6 reflects the interval where 5.50 sits, but the precise prediction is 5.50. If other options had claimed specific values or broader claims about the population or sample, those would require additional context beyond this single prediction.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 1B

The regression model equation for your sample of data is Ŷi = 7.42 – 0.64Xi, as shown in the graph below. When X equals 3, what can you say about the predicted value of the dependent variable Y (i.e., Ŷ)?

查看解析

登录即可查看完整答案

类似问题

For the simple linear regression model, the parameter values of the model are calculated by minimize the

Question at position 38 DAEBC

Question at position 36 BCEAD

Question at position 33 CADEB

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单