The following table summarizes a random sample of 10 weeks...

The following table summarizes a random sample of 10 weeks comparing average temperature with the number of gallons of ice cream sold that week by a restaurant. Temperature Ice Cream Sold (Gal) 73 110 65 95 81 135 90 160 75 97 77 105 82 120 93 175 86 140 79 121 a) Find the correlation coefficient. Use the correlation coefficient to determine the following about the relationship between the variables temperature and number of gallons of ice cream sold. Form: ________________________ Direction: ______________________ Strength: ________________________ b) Find the linear regression equation. Write it in the form y=ax+b c) Use the appropriate information to predict the number of gallons of ice cream sold when the temperature is 92 degrees Fahrenheit. d) Find the coefficient of determination and interpret it

Transcript

00:01 Once again, welcome to a new problem.

00:05 This time we're dealing with regression.

00:07 And when it comes to regression, we have the relationship.

00:13 So we're looking at the relationship between a typical x variable, and the x variable is the independent variable.

00:24 And sometimes we do call the independent variable, the explanatory variable.

00:31 So we call it the explanatory variable.

00:34 The other variable we're looking at is the dependent variable.

00:40 And the dependent variable, that's your typical y variable.

00:45 And we do call this the response variable.

00:51 So you do have the response variable.

00:53 The typical regression equation that shows the relationship between the x and the y variable is the same as y hat equals to beta not plus a beta 1x or sometimes you can see it in terms of y equals to a plus bx where beta 1 is the slope and beta not is the intercept so we have the slope and the intercept and we have the correlation coefficient so correlation for a typical relationship between x and y variables and what the correlation coefficient does.

01:38 It's the r value and it runs from negative 1 to 0 up until 1 where we have no relationship.

01:49 We have no relationship and at 1 we have a perfect positive relationship.

01:59 Perfect positive relationship at negative one we have a perfect perfect negative relationship and anything close to zero is a weak relationship and anything between say 0 .6 up until 0 .7 for example this would be a moderate relationship.

02:35 So the moderate relationship between your typical x and y variable.

02:40 Also the correlation coefficient has an equation showing summations of x, summation of x, summation of y, summation of x squared, summation of x squared, summation of y squared, summation of y squared, formula for any specific problem.

03:05 We're looking at comparisons between the average temperature, and this is in degrees fahrenheit, with the number of gallons of ice cream.

03:16 So this is ice cream sold, the number of gallons of ice cream, and the column, we have the temperature column and the ice cream sold column on both options.

03:28 The first step is we want to determine the correlation, coefficient so when we run the numbers for the correlation coefficient plugging in specific values within the formula what's going to happen is we're going to get the r value to be equivalent to 0 .9291 so 0 .9291 so 0 .9291 and then the the next step is we want to determine the direction and strength of the correlation coefficient...

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