True or False For each of the following statements choose ei

True or False? For each of the following statements, choose either true or false.

T F The symbols, 0 and 1, represent the sample intercept and slope, respectively.

T F For dierent values of an explanatory variable the simple linear regression model describes how the predicted value (or mean) of the response variable changes.

T F The null hypothesis, H0 : 1 = 0, claims that there is no linear relationship between y and x.

T F The test statistic for testing the null hypothesis, H0 : 1 = 0, follows a tdistribution with n1 degrees of freedom.

T F When we t a least-squares regression line to two quantitative variables, we select the line that minimizes the sum of squared horizontal distances between the data points and their corresponding predictions.

T F If we switch the role of the response and explanatory variable the least squares estimate of the slope will not change.

Solution

Q1.
T F The symbols, 0 and 1, represent the sample intercept and slope, respectively.
[ANSWER] TRUE
Y = bo + b1 X, where bo= intercept, b1 = slope
  

Q2.
T F For diferent values of an explanatory variable the simple linear regression model describes how the predicted value (or mean) of the response variable changes.
[ANSWER] TRUE
Y = bo + b1 X, predicted value = b0 + b1(explanatory variable) , fr every diffrent value of explanatory variable, the predicted value changes

Q3.
T F The null hypothesis, H0 : 1 = 0, claims that there is no linear relationship between y and x.
[ANSWER] FALSE
Ho: linear relationship between y and x
H1: No linear relationship between y and x

Q4.
T F The test statistic for testing the null hypothesis, H0 : 1 = 0, follows a tdistribution with n1 degrees of freedom.
[ANSWER] True