# Stanford University Statistical Learning Quiz Answer | Linear Regression

**Stanford University Statistical Learning Quiz Answer |**

**Linear Regression**

In this article i am gone to share Stanford University Statistical Learning Quiz Answer | Linear Regression with you..

**Simple Linear Regression Quiz**

### 3.1.R1

**Why is linear regression important to understand? Select all that apply:**

- The linear model is often

- Linear regression is very extensible and can be used to capture nonlinear effects

- Simple methods can outperform more complex ones if the data are noisy

- Understanding simpler methods sheds light on more complex ones

### 3.1.R2

**You may want to reread the paragraph on confidence intervals on page 66 of the textbook before trying this queston (the distinctions are subtle).**

**Which of the following are true statements? Select all that apply:**

- A 95% confidence interval is a random interval that contains the true parameter 95% of the time

- The true parameter is a random value that has 95% chance of falling in the 95% confidence interval

- I perform a linear regression and get a 95% confidence interval from 0.4 to 0.5. There is a 95% probability that the true parameter is between 0.4 and 0.5.

- The true parameter (unknown to me) is 0.5. If I sample data and construct a 95% confidence interval, the interval will contain 0.5 95% of the time.

**Hyphotesis Testing and Confidence Invervals Quiz**

### 3.2.R1

**We run a linear regression and the slope estimate is 0.5 with estimated standard error of 0.2. What is the largest value of for which we would NOT reject the null hypothesis that beta_1=b? (assume normal approximation to t distribution, and that we are using the 5% significance level for a two-sided test; need two significant digits of accuracy)**

- 0.892

### 3.2.R2

**Which of the following indicates a fairly strong relationship between X and Y?**

- R^2 = 0.9
- The p-value for the null hypothesis beta_1=0 is 0.0001
- The t-statistic for the null hypothesis beta_1=0 is 30

**Multiple Linear Regression Quiz**

### 3.3.R1

**Suppose we are interested in learning about a relationship between X_1 and Y, which we would ideally like to interpret as causal.**

**True or False? The estimate hatbeta_1 in a linear regression that controls for many variables (that is, a regression with many predictors in addition to X_1) is usually a more reliable measure of a causal relationship than hatbeta_1 from a univariate regression on X_1.**

- True

- False

### 3.4.R1

**According to the balance vs ethnicity model, what is the predicted balance for an Asian in the data set? (within 0.01 accuracy)**

- 512.31

### 3.4.R2

**What is the predicted balance for an African American? (within .01 accuracy)**

- 531

**Extensions of the linear model**

### 3.5.R1

**According to the model for sales vs TV interacted with radio, what is the effect of an additional $1 of radio advertising if TV=$50? (with 4 decimal accuracy)**

- .0839

### 3.5.R2

**What if TV=$250? (with 4 decimal accuracy)**

- .3039

**Linear Regression in R**

### 3.R.R1

**What is the difference between lm(y ~ xz) and lm(y ~ I(xz)), when x and z are both numeric variables?**

- The first one includes an interaction term between x and z, whereas the second uses the product of x and z as a predictor in the model.

- The second one includes an interaction term between x and z, whereas the first uses the product of x and z as a predictor in the model.

- The first includes only an interaction term for x and z, while the second includes both interaction effects and main effects.

- The second includes only an interaction term for x and z, while the first includes both interaction effects and main effects.

**Chapter 3 Quiz**

**Which of the following statements are true?**

- In the balance vs. income * student model plotted on slide 44, the estimate of beta3 is negative.

- One advantage of using linear models is that the true regression function is often linear.

- If the F statistic is significant, all of the predictors have statistically significant effects.

- In a linear regression with several variables, a variable has a positive regression coefficient if and only if its correlation with the response is positive.