Refer to the data on happiness and age to answer the following questions. Happiness Age 62 49 66 51 : : 72 69 Click here for the Excel Data File a. Estimate a simple linear regression model with happiness as the response variable and age as the explanatory variable. (Round your answers to 2 decimal places.) Happiness = [ ] + [ ] Age b. Use the sample regression equation to predict Happiness when Age equals 25, 50, and 75. (Round coefficient estimates to at least 4 decimal places and final answers to 2 decimal places.) Age Happiness 25 [ ] 50 [ ] 75 [ ] c-1. A scatterplot of Happiness and Age is shown below.
Added by Isabel J.
Close
Step 1
First, we need to find the simple linear regression model, which is in the form of $Happiness = \beta_0 + \beta_1 \cdot Age$. To do this, we need to calculate the coefficients $\beta_0$ and $\beta_1$. Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 86 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A survey asks questions about one's happiness and health. One would think that health plays a role in one's happiness. Use the data in the accompanying table to determine whether healthier people tend to also be happier. Treat level of health as the explanatory variable. Create a conditional distribution for the data. Level of Happiness | Level of Health: Poor | Level of Health: Fair | Level of Health: Good | Level of Health: Excellent Not too happy | | | | Pretty happy | | | | Very happy | | | | Total | | | | (Round to three decimal places as needed.) Data table | Poor | Fair | Good | Excellent Not too happy | 696 | 1,386 | 1,629 | 732 Pretty happy | 950 | 3,817 | 9,642 | 5,195 Very happy | 345 | 1,372 | 4,520 | 5,095
Jon S.
A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. Estimate: Happiness = β0 + β1 Age + ε. (Round your answers to 2 decimal places.) Happiness = [ ] + [ ] Age. b-1. Choose the hypotheses to determine if age has an impact on happiness. H0: β1 = 0; HA: β1 ≠0 H0: β1 < 0; HA: β1 > 0 H0: β1 > 0; HA: β1 < 0 b-2. Calculate the value of the test statistic. (Round answer to 2 decimal places.) Test statistic: [ ] b-3. Find the p-value: ○ p-value < 0.01 ○ 0.01 ≤ p-value < 0.025 ○ 0.025 ≤ p-value < 0.05 ○ 0.05 ≤ p-value < 0.10 ○ p-value ≥ 0.10 c. At the 1% significance level, is Age significant in explaining Happiness? No, since we do not reject the null hypothesis. Yes, since we do not reject the null hypothesis. No, since we reject the null hypothesis. Yes, since we reject the null hypothesis.
Sri K.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD