The chairman of the marketing department at a large state university undertakes

ID: 3224572 • Letter: T

Question

The chairman of the marketing department at a large state university undertakes a study to relate starting salary (y) after graduation for marketing majors to grade point average (GPA) in major courses. To do this, records of seven recent marketing graduates are randomly selected. The MegaStat output of a simple linear regression analysis of the data set for this case is given in table (below).

Find the least squares point estimates b0 and b1 of 0 and 1 on the output and report their values. (Round your answers for b0 to 3 decimal places and b1 to 4 decimal places.)

Find the t statistic for testing the significance of the slope on the output and report their values. (Round your answers for sb1 to 4 decimal places and t to 2 decimal places.)

Using the t statistic and appropriate critical value, test H0: 1 = 0 versus Ha: 1 0 by setting equal to .05. Is the slope (regression relationship) significant at the .05 level?

Reject or don't reject H0, what type of evidence of a significant relationship between x and y (extremely strong, very strong, strong, some, no)

Using the t statistic and appropriate critical value, test, H0: 1 = 0 versus Ha: 1 0 by setting equal to .01. Is the slope (regression relationship) significant at the .01 level?

Reject or don't reject H0, what type of evidence of a significant relationship between x and y (extremely strong, very strong, strong, some, no)

Find the p-value for testing H0: 1 = 0 versus Ha: 1 0 on the output and report its value. Using the p-value, determine whether we can reject H0 by setting equal to .10, .05, .01, and .001. How much evidence is there that the slope (regression relationship) is significant? (Round your answers for p-value to 3 decimal places.)

Reject at =

what type of evidence of a significant relationship between x and y (extremely strong, very strong, strong, some, no)

Find t statistic for testing the significance of the y intercept on the output and report their values. (Round your answers for t to 2 decimal places.)

Find the p-value for testing H0: 0 = 0 versus Ha: 0 0. Using the p-value, determine whether we can reject H0 by setting equal to .10, .05, .01, and .001. What do you conclude about the significance of the y intercept? (Round your answers for p-value to 3 decimal places.)

Reject at =

what type of evidence that the y-intercept is significant (extremely strong, very strong, strong, some, no)

Explanation / Answer

Solution

y = starting salary after graduation for marketing majors

x = grade point average (GPA) in major courses

Back-up Theory

Regression model: y = 0 + 1x +

The least square estimate of 0 and 1 are respectively b1 and b2.

The intercept is represented by b0 and b1represents the slope.

Now, to work out solution,

Part (a)

The least square estimate of 0 and 1

From the given ‘Regression Output’ table, b0 = 14.816 and b1= 5.7066 ANSWER

Part (b)

Test statistic for significance of the slope (b1) [i.e., to test 1 = 0], is t = | b1– 0|/SE(b1)

= 5.7066/0.3953 [refer to ‘Regression Output’ table]

= 14.4361 = 14.44 ANSWER

Part (c)

To test H0 : 1 = 0 Vs HA : 1 0 at = 0.05, test statistic t = 14.4361 as obtained in

Part (b).

From ‘Regression Output’ table, p-value = 2.88-E-05 which is much smaller than 0.05, So, H0 is rejected.

A very low p-value suggests that the the relationship is extremely significant. ANSWER

Part (d)

To test H0 : 1 = 0 Vs HA : 1 0 at = 0.01, test statistic t = 14.4361 as obtained in

Part (b).

From ‘Regression Output’ table, p-value = 2.88-E-05 which is much smaller than 0.01, So, H0 is rejected.

A very low p-value suggests that the slope is extremely significant. ANSWER

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The chairman of the marketing department at a large state university undertakes

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